Systems and methods for coordinated editing of seismic data in dual model

ABSTRACT

A system and method may model physical geological structures. Seismic and geologic data may be accepted. A three-dimensional (3D) transformation may be generated between a 3D present day model having points representing present locations of the physical geological structures and a 3D past depositional model having points representing locations where the physical geological structures were originally deposited. An indication may be accepted to locally change the 3D transformation for a subset of sampling points in a first model of the models. The 3D transformation may be locally changed to fit the updated subset of sampling points. A locally altered or updated version of the first model and, e.g., second model, may be displayed where local changes to the first model are defined by the locally changed 3D transformation. The transformation may also be used to extract geobodies in the past depositional model.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/669,454 filed Aug. 4, 2017, issued as U.S. Pat. No. 10,013,800, whichis a continuation of Ser. No. 15/166,438, filed May 27, 2016, issued asU.S. Pat. No. 9,728,003, which is a continuation of U.S. patentapplication Ser. No. 14/860,084, filed Sep. 21, 2015, issued as U.S.Pat. No. 9,355,494, which is a continuation of U.S. patent applicationSer. No. 14/260,760, filed Apr. 24, 2014, issued as U.S. Pat. No.9,142,059, which is a continuation of U.S. patent application Ser. No.12/909,981, filed Oct. 22, 2010, issued as U.S. Pat. No. 8,743,115,which claims the benefit of prior U.S. Provisional Application Ser. No.61/254,438, filed Oct. 23, 2009, all of which are incorporated herein byreference in their entirety.

FIELD OF THE INVENTION

The invention pertains to the general field of modeling stratifiedterrains in the subsurface.

The invention pertains to generating a first present day modelrepresenting stratified terrains and generating a second correspondingdepositional model representing the stratified terrains at thegeological-time at which they were originally deposited within theEarth.

BACKGROUND OF THE INVENTION

Erosion and tectonic activity through time transform an initiallyuniform stratified terrain composed of a continuous stack of levelsurfaces to a terrain fractured by faults forming discontinuities acrossthe originally continuous horizons. Accordingly, to model the subsurfaceat the original time of deposition from seismic data (e.g., associatedwith seismic cubes) and/or geologic data (e.g., associated with wellmarkers along well paths) collected from the present day subsurfacestructures (e.g., to “reverse time”), the model may simulate a reversalof such the erosion and tectonic activity.

However, modeling mechanisms used to generate models at the originaltime of deposition often use extensive simplifications and the data usedto generate models may have significant uncertainties, thereby renderingthe models inaccurate.

Accordingly there is a need in the art to more accurately model presentday structures at a geological-time when they were originally depositedand to correct errors in that model.

SUMMARY OF THE INVENTION

Embodiments of the invention provide a system and method for modelingstratified terrains of a geological subsurface at the time of geologicaldeposition. e.g., including geological horizons and faults.

Embodiments of the invention provide a system and method for generatingmodels representing both the geometry of geological structures, e.g.,horizons, and geological properties of those structures. Models may begenerated by incrementally modifying horizons and faults to provide anaccurate model even in the presence of non vertical faults.

Embodiments of the invention provide a system and method forinteractively editing the location or physical property values of pointsin a present day or recent geological model (in “G space”) or in acorresponding past depositional model (in “G* space”), the pointsrepresenting physical subsurface structures. Geological models in Gspace and/or G* space may be, for example, a digital rendering ofseismic and geologic data, e.g., defined by cells, nodes, vertices,facets, voxels, pixels, etc., that estimate or approximate the likelyposition of groups of underground particles. A transformation maydefined a relationship between the present day model in G space and pastdepositional models in G* space. Embodiments of the invention mayinclude, when the location or properties of points in either model aremodified, automatically modifying the corresponding points in the othermodel accordingly. In this way, a user may interact or edit adepositional time model (where structures and properties are uniformlydistributed) and the user may view the corresponding edits implementedin the present day complex faulted model, where such edits would bedifficult to implement, e.g., particularly across faults.

Embodiments of the invention provide a system and method for modellingphysical geological structures. Seismic data may be accepted. A globaltransformation may be generated between a present day model havingpoints representing present locations of the physical geologicalstructures and a past depositional model having points representinglocations where the physical geological structures were originallydeposited. The global transformation may be a three dimensional (3D)transformation, which may be generated, for example, by functions thatare continuous everywhere except across faults. An indication may beaccepted, e.g., from a user, to change the global transformation for asubset of sampling points in the models. The global transformation forthe subset of sampling points may be updated. An updated version of atleast one of the models may be displayed.

Embodiments of the invention provide a system and method forsimultaneously editing corresponding models representing the samephysical geological structures. Seismic data (e.g., associated with eachseismic cube) and/or geologic data (e.g., well markers along well paths)may be accepted. A first model and a second model may be displayed. Onemodel may represent present day locations of the physical geologicalstructures and the other model may represent locations where thephysical geological structures were originally deposited in the past.The first and second models may be related by a 3D transformation basedon at least three functions continuous everywhere except across faults.Graphical user input may be accepted (e.g., via an input device,keyboard, mouse, etc.) for editing property values assigned to a firstsubset of points of the first model. The same edited property values maybe automatically assigned to a second subset of points of the secondmodel, wherein the second subset of points are the image of the firstsubset of points as defined by the transformation between the first andsecond models. The second subset of points in the second model may bedisplayed with the automatically assigned property values.

BRIEF DESCRIPTION OF THE DRAWINGS

The principles and operation of the system, apparatus, and methodaccording to embodiments of the present invention may be betterunderstood with reference to the drawings, and the followingdescription, it being understood that these drawings are given forillustrative purposes only and are not meant to be limiting.

FIG. 1 is a schematic illustration of a uvt-transformation between apresent day geological model and a past depositional model in respective3D spaces according to an embodiment of the invention;

FIG. 2 is a schematic illustration of a curvilinear uvt coordinatesystem used for transforming points between the two 3D spaces of FIG. 1non-linearly, according to an embodiment of the invention;

FIG. 3 is a schematic illustration of an exploded and collapsed view ofa present day geological model decomposed into tetrahedral cellsaccording to an embodiment of the invention;

FIG. 4 is a schematic illustration of the present day and pastdepositional models of FIG. 1, to which geological property values areassigned according to an embodiment of the invention;

FIG. 5 is a schematic illustration of a faulted and a flattened seismiccube of the present day and past depositional models of FIG. 1,respectively, according to an embodiment of the invention:

FIG. 6 is a schematic illustration of a 3D seismic window of the faultedseismic cube of FIG. 5 used to automatically generate additional pointsto add to the present day model according to an embodiment of theinvention:

FIG. 7 is a schematic illustration of visualizations of a geobodydisplayed in two separate views on horizons of faulted and flattenedseismic cubes, respectively, according to an embodiment of theinvention;

FIG. 8 is a schematic illustration of visualizations of a geobodypainter editing tool displayed in two separate views on horizons of thefaulted and flattened seismic cubes of FIG. 5, respectively, accordingto an embodiment of the invention;

FIG. 9 is a schematic illustration of a system according to anembodiment of the invention; and

FIGS. 10-11 are flowcharts of methods according to embodiments of theinvention.

For simplicity and clarity of illustration, elements shown in thedrawings have not necessarily been drawn to scale. For example, thedimensions of some of the elements may be exaggerated relative to otherelements for clarity. Further, where considered appropriate, referencenumerals may be repeated among the drawings to indicate corresponding oranalogous elements throughout the serial views.

DETAILED DESCRIPTION

For the sake of clarity and for the purpose of simplifying thepresentation of embodiments of the invention, the following preliminarynon-limiting descriptions are given.

Geological-Time

A particle of sediment in a geological terrain may be observed at alocation in the subsurface. The location of the particle may bemathematically represented or modeled, e.g., by a vector, (x,y,z), in athree-dimensional (3D) space, such as the Cartesian coordinate system(of course, when modelling such particles, the position of manyparticles may be modeled together as for example using a cell). Whenmodeled, a data structure such as a node or cell may representparticles. The locations of the points or data structures in the modelmay be estimates and approximations of the real locations of theparticles they represent, which may have some error. The time when theparticle of sediment was originally deposited may be referred to as the“geological-time” and may be represented or modeled, e.g., as ageological-time function of the present day location of the particle,t(x,y,z). When used herein, a “present day” location for a particle (ordata structure representing one or more particles) or subsurface featuremay mean the location of the item in the current geological time period(not necessarily exactly today's date), relative to geological time. Theactual geological-time of the deposition of particles may be difficultto determine and may be replaced, e.g., by any arbitrary monotonicincreasing function of the actual geological-time. The geological timefunction t(x,y,z) may instead provide the relative times or time orderwhen structures were deposited (e.g., a greater (t) value correspondingto relatively younger, more recently deposited structures), notnecessarily the real times. The monotonic function may be referred to asthe “pseudo-geological-time”. Geological-time and pseudo-geological-timeare referred to interchangeably herein.

Horizon, Fault and Unconformity

In stratified layers, horizons, faults and unconformities may becurvilinear surfaces which may be for example characterized as follows:

-   -   A horizon, H(t), may be a surface corresponding to a plurality        of particles of sediment which were deposited approximately at        substantially the same geological-time, t.    -   A fault may be a surface of discontinuity of the horizons that        may have been induced by a relative displacement of terrains on        both sides of such surfaces. In other words, the        geological-time (t) of deposition of the sediments is        discontinuous across each fault. Faults may cut horizons and may        also cut other faults.    -   An unconformity may be a surface of discontinuity of the        horizons that may have been induced by for example an erosion of        old terrains replaced by new ones. In other words, similarly to        faults, the geological-time (t) of deposition of the sediments        is discontinuous across each unconformity. When discussed        herein, unconformities are treated as faults: as a consequence,        in this patent application, faults may include both real faults        and unconformities.        Reference Horizons and Control-Points

The geological domain may be characterized by a series of “referencehorizons” {H(t₁),H(t₂), . . . ,H(t_(n))}, which may be separategeological layers with significantly distinct physical properties andassociated with distinct geological-times of deposition {t₁,t₂, . . .,t_(n)}, respectively. When discussed herein, the horizons areimplicitly assumed to be sorted according to their geological-times ofdeposition so that H(t₁) is assumed to correspond to the older sedimentsand H(t_(n)) to the younger. In other words, the deposition time t_(i)of H(t_(i)) is older than the deposition time t_(i+1) of H(t_(i+1)). Inpractice, each reference horizon H(t_(i)) is observed on a set ofsampling points referred to as “control-points” at which thegeological-time function may approximate t_(i) as closely as possible.Control-points may be a set of points generated from seismic data andwell data which have been identified, e.g., automatically by a computerand/or manually by a user, as representing to the same horizon, fault,or other geological structure.

Level Surface (Also Referred to as “Iso-Surface”)

The geological domain may be defined in a 3D space by a given functionof geological-time, t(x,y,z). The geological-time function t(x,y,z) maybe monotonic, i.e., the gradient of the geological-time does not vanishand the function has no local maximum or minimum values. A levelsurface, H(t₀), may be the set of points where the geological-timet(x,y,z) is equal to a given numerical value, t₀. Therefore, if thegeological-time t(x,y,z) represents a pseudo-geological-time ofdeposition, then the level surface H(t₀) of t(x,y,z) may be a geologicalhorizon. Level surfaces may also be referred to as “isovalue-surfaces”or, simply, “iso-surfaces”. In one embodiment of this invention, thegeological time may be defined at the vertices of a mesh, lattice orgrid (e.g., a tetrahedral mesh) and the iso-value surfaces may beextracted, according to mechanisms known in the art.

Various mechanisms are currently used for modeling subsurface geologicalterrains:

GeoChron Model and Uvt-Transform

When a layer of particles was deposited during a certain geological-timeperiod in the past, the layer typically had uniform properties, such asparticle density, porosity, etc. However, through time, the layers erodeand are disrupted by faults, tectonic motion or other sub-surfacemovements, which result in uneven and discontinuous layers. As comparedto the uniform layers of the past, the discontinuous layers of thepresent are difficult to model.

Accordingly, the “GeoChron” model has recently been developed to operatebetween two 3D spaces, for example:

-   -   A 3D space, G, representing a geological model of the present        day subsurface features (e.g., current or recent modeled        locations of particles of sediment in the terrain). The modeled        location of each particle may be represented by the coordinates        (x,y,z), where (x,y) describes the geographical coordinates of        the particle (e.g., latitude and longitude) and (z) describes        the altitude or distance below a surface level; and    -   A 3D space. G*, representing a geological model of locations of        particles of sediment at the time when the particles were        originally deposited. The modeled location of each particle may        be represented by the coordinates (u,v,t) where (t) is the        pseudo-geological-time of deposition of the particle and (u,v)        is the paleo-geographical coordinates of the particle at        geological-time (t).

The GeoChron model defines a transformation between the two 3D spaces Gand G*. The transformation may be referred to as a “uvt-transformation”.The GeoChron model applies a forward uvt-transformation to transform thepresent day model (a model of the subsurface features in present orrecent time) in G space to the original deposition model in G* space andapplies an inverse uvt-transformation to transform the originaldeposition model in G* space to the present day model in G space.Accordingly, a processor applying the GeoChron model may execute complexcomputations on the original deposition model in G* space wheregeological properties are typically uniform and simple to manipulaterelative to the discontinuous present day model in G space. Once theoriginal deposition model is sufficiently accurate, the GeoChron modelmay be used to transform the model back to the present day time domainto generate the present day model.

Other subsurface models and other transforms between present day andpast models may be used with embodiments of the present invention.

When used herein, “generating” or “creating” a model or a subsurfacefeature may include creating (e.g., using a computer processor) datarepresenting the model or feature, the data being stored for example ina computer system such as that shown in FIG. 9.

Reference is made to FIG. 1, which schematically illustrates auvt-transformation between two 3D spaces G 104 and G* 106 according toan embodiment of the invention.

The “forward” or “direct” uvt-transformation 100 defines parametricfunctions 102 {u(x,y,z),v(x,y,z),t(x,y,z)}, which transform each point(x,y,z) of the geological G space 104 to a point{u(x,y,z),v(x,y,z),t(x,y,z)} in the depositional G* space 106. Theforward uvt-transformation 100 may be represented, for example, asfollows:(x,y,z)

{u(x,y,z),v(x,y,z),t(x,y,z)}  [1]A processor using the forward uvt-transformation 100 transforms eachhorizon H(t) (e.g., 108 a or 108 b) of model 108, in the G space 104,into a level horizontal plane H*(t) (e.g., 110 a and 110 b,respectively) of model 110 in the G* space 106. In the G* space 106,horizons 110 a and 110 b of model 110 are simply the level surfaces ofthe function t(x,y,z) representing the geological-time at location(x,y,z) in the G space. That is, since a horizon models a set ofparticles of sediment that was uniformly deposited in time, each horizonis constant at the time when the particles modeled thereby wereoriginally deposited (e.g., in G* space 106). Therefore, each horizon110 a and 110 b in G* space 106 may be uniquely defined by a singletime. (t). The forward uvt-transformation 100 removes faults F(t) 109(e.g., 109 a. 109 b, 109 c, . . . ) of model 108, in the G space 104, byjoining corresponding fault edges of model 110 in the G* space 106,thereby simulating the reversal the effects of erosion and tectonicactivity through time.

Conversely, the “inverse” or “reverse” uvt-transformation 112 definesparametric functions 114 {x(u,v,t), y(u,v,t), z(u,v,t)}, which aprocessor may use to transform each point (u,v,t) of the depositional G*space 106 to a point {x(u,v,t), y(u,v,t), z(u,v,t)} in the geological Gspace 104.

The inverse uvt-transformation 112 may be represented, for example, asfollows:(u,v,t)

{x(u,v,t),y(u,v,t),z(u,v,t)}  [2]In practice, such a reverse transformation may be restricted to a partG*₀ of the G* space called the holostrome and corresponding to theparticles of sediment which can actually be observed today in the Gspace.

As shown in [1], uvt-transformation 100 transforms each point (x,y,z) inpresent day G space 104 independently in each of the (three) differentcoordinates (u,v,t) in depositional G* space 106, for example, usingthree independent functions {u(x,y,z), v(x,y,z), t(x,y,z)}. Thus,uvt-transformation 100 is a three-dimensional (3D) transformation.Similarly, inverse uvt-transformation 112, e.g., shown in equation [2],transforms each point (u,v,t) in depositional G* space 106 independentlyin each of the (three) different coordinates (x,y,z) in present day Gspace 104, for example, using three independent functions {x(u,v,t),y(u,v,t), z(u,v,t)}. Thus, inverse uvt-transformation 112 is a 3Dtransformation. Transformations 100 and 112 may be considered as theforward and reverse components of the same transformation.Transformations 100 and 112 may be considered “global” transformationssince the same transformation. e.g., a vector field or interpolation,operates on a region or all points in models 108 and/or 110. In someembodiments, the inverse (or reverse) uvt-transformation 112 may only bedefined (e.g., with a non-trivial identity transformation) in regions ofG*space 106 not affected by erosion or other predefined types ofgeological activity. It may be noted that, contrary to othertransformations (referred to as “xyt-transforms”), which transform(x,y,z) coordinates to (x,y,t) coordinates leaving two dimensions (x)and (y) unchanged and only transforming 1D (a simple verticalstretching) from the z-axis to a t-axis, the uvt transformation may movepoints in three dimensions (e.g., with three degrees of freedom) and,for example, correctly works even in the presence of non-vertical faults(e.g., faults having a range of x and y values).

Using the forward uvt-transformation 100. e.g., defined in equation (1),and the inverse uvt-transformation 112, e.g., defined in equation (2),any geological property may be modeled in one of the two spaces (G space104 or G* space 106) and the result of the property modeled in one spacemay be transferred to the other space (G* space 106 or G space 104,respectively). In practice, a geological property is typically modeledin the space where modeling the property is the simplest.

Model 108 (of FIG. 1) defined by the functions u(x,y,z), v(x,y,z) andt(x,y,z) may be piecewise continuous. Typically, the onlydiscontinuities of these functions may represent subsurface fracturesinduced by fault surfaces. At the geological-time of deposition of theparticles of sediment, before faulting induced by tectonic eventsoccurred, the subsurface layers were continuously formed and maytherefore be represented by model 110 defined by functions u(x,y,z),v(x,y,z) and t(x,y,z) that are likewise continuous. Therefore, presentday model 108, which may be a transformation of these continuousfunctions, may “inherit” such a paleo-continuity across faults surfacesin the model. Modelling such behavior of functions u(x,y,z) and v(x,y,z)across the faults in model 110 may be used to more accurately constructthese functions across the faults in the present day model 108. In theGeoChron model, the fault structure may be known prior to generating thetransformation functions and may be integrated into the functions asconstraints.

Representations of present day model 108 in G space 104 and itsuvt-transformation 100 image depositional model 110 in G* space 106 maybe displayed to a user on a monitor, e.g., display 980 of FIG. 9.

Reference is made to FIG. 2, which schematically illustrates acurvilinear uvt coordinate system that transforms the non-uniformpresent day model 108 in G space 104 to generate the uniform model 110in G* space 106 according to an embodiment of the invention. Thecurvilinear uvt coordinate axes represent the curvilinear deformationused to transform level surfaces in G space 104 to constant orhorizontal sections in G* space 106. The uvt coordinate axes having anorthogonal shape in G* space 106 have a curvilinear shape in G space104.

An orthogonal uvt coordinate system in G* space 106 may be defined sothat the intersections of level surfaces in G space 104 are mapped toconstant values of u, v and t under the uvt transformation. Such a uvtcoordinate system may have a curvilinear shape when viewed in the Gspace 104. For example, under the uvt transformation:

-   -   a curvilinear u-axis intersecting a point (x,y,z) may correspond        to the intersection of the iso-v and iso-t level surfaces        crossing at point (x,y,z);    -   a curvilinear v-axis intersecting a point (x,y,z) may correspond        to the intersection of the iso-u and iso-t level surfaces        crossing at point (x,y,z); and    -   a curvilinear t-axis intersecting a point (x,y,z) may correspond        to the intersection of the iso-u and iso-v level surfaces        crossing at point (x,y,z).

In some embodiments:

-   -   The curvilinear t-axis may correspond to a set of points in G        space 104 which were deposited at the same (u,v)        paleo-geographic coordinates. Accordingly, the curvilinear        t-axis may be referred to as an “Iso-Paleo-Geographic line” or,        simply, an “IPG-line”.    -   IPG-lines and the u and v curvilinear axes are discontinuous        across faults.    -   IPG-lines in G space 104 may be transformed to vertical        straight-lines in G* space 106 under the uvt transformation.        The xyt-Transform

Computing the (u,v) paleo-geographic coordinates described above mayinclude solving a complex system of coupled differential equations. Tobypass the difficult problem, modeling mechanisms known in the artavoided the uvt transformation and instead used a simplertransformation, a “xyt-transform”. The xyt-transform may be defined by asimple parameterization of the x,y,z coordinates, for example, asfollows:u=f(x,y,z)=x and v=g(x,y,z)=ywhere parametric functions f(x,y,z) and g(x,y,z) are defined by thepresent day geographic coordinates x and y. The level surfaces of thefunctions f(x,y,z) and g(x,y,z) are typically vertical planes whoseintersections are vertical lines. Such a definition implies that,contrary to the uvt transformation above, under the xyt transformationthe IPG lines in G space 104, i.e., the set of points in G space 104which were deposited at the same coordinates f(x,y,z) and g(x,y,z) i.e.,the same coordinates x and y, are vertical straight-lines continuousacross the faults. Such an approach may provide for example thefollowing drawbacks:

-   -   In the presence of a reverse fault, several particles of        sediment modeled in the present day model 108 in G space 104 and        located at multiple intersections of a vertical straight-line        through (x0,y0) and a horizon H(t) will have exactly the same        paleo-geographic coordinates (f(x,y,z)=x0,g(x,y,z)=y0,t).        Accordingly, the xyt transformation models these multiple        distinct particles of sediment in exactly the same location in        the xyt transformed space. This is clearly an error since two        distinct particles of sediment observed today in G space cannot        have been deposited at the same location and time.    -   In the presence of a normal fault, a vertical line through        (x0,y0) may intersect the fault and not intersect a given        horizon H(t). As a consequence, the point        (f(x,y,z)=x0,g(x,y,z)=y0,t) in the depositional xyt        transformation space may have no reverse image by reverse        xyt-transform back to the present day G space. This induces        holes in the depositional xyt transformation space. This is        clearly an error since each particle of sediment observed today        in G space must have been deposited and therefore must exist        somewhere in the depositional xyt transformation space.

Since under the xyt transform, reverse faults in the present day modelgenerate duplicate points in the depositional model and normal faults inthe present day model generate holes in the depositional model, onlyperfectly vertical faults in present day models may be correctly modeledat the time of deposition. Since vertical faults are extremely rare, thexyt transformation is highly inaccurate.

Under the uvt-transformation point along both normal and reverse faultsin the present day may be correctly modeled by a one-to-onecorrespondence with points in the depositional models thereby avoidingthe aforementioned inaccuracies of the xyt transformation.

While the xyt transform is imperfect, embodiments of the invention maybe used in combination therewith.

Wheeler Model

The Wheeler model, introduced by H. Wheeler in the 1950's, representsgeological terrains at depositional geological-time. The practicalimplementations of the Wheeler model are implicitly based onxyt-transforms. Accordingly, as described above, this simplifiedapproach is only accurate in the particular (and improbable) case whereall the faults are strictly vertical. However, while the Wheeler modelis imperfect, embodiments of the invention may be used in combinationtherewith.

Virtual Camera

A “virtual camera” may be a graphical device or tool executed by orproduced by a computer (e.g., computing system 905 of FIG. 9) forgenerating visualizations of geological numerically models. A virtualcamera may include a software module which when executed transformsnumerical encoding of geological structures into a visualization orimage. In one non-limiting example, these images may be displayed in twodimensions (2D) on a screen of a computer or in three dimensions (3D) ona 3D device such as a cave such as a 3D chamber having vertically andhorizontally oriented screens (e.g., a room where the walls, ceiling andfloor are screens).

Seismic Cube Grid (SG) and Properties

A seismic cube, also referred to as a “seismic-grid” (SG), may be aregular three dimensional structured grid, for example, defined asfollows:

-   -   The edges of seismic cube grid SG may be rectilinear, orthogonal        to each other, and parallel to a (x,y,z) rectilinear coordinate        system:        -   The x and y axes may define a horizontal plane of a present            day geographical coordinate system in G space 104.        -   The z axis may define a vertical direction and may represent            depth, altitude or seismic geological time varying in the            vertical direction.    -   Cells of seismic cube grid SG may be hexahedral (e.g., cubic)        and are preferably uniform in size in the x, y and z directions.    -   Each cell C of seismic cube grid SG may be defined by the        coordinates x(C), y(C) and z(C), e.g., at the center of the cell        C:        -   x(C) may be referred to as the “in-line” coordinate of C,        -   y(C) may be referred to as the “cross-line” coordinate of C,    -   A column of cells, each corresponding to a single pair (x,y) of        in-line and cross-line coordinates and having different (z)        coordinates, may be referred to as a seismic trace.

These cells may correspond to or represent estimates or approximationsof the position of individual and groups of actual subsurface particles.

The amplitude of a seismic signal may be measured and sampled at thecenters x(C), y(C) and z(C) of all cells C along each seismic-trace ofseismic cube grid SG. For each seismic-trace corresponding to a singlepair (xi,yj) of in-line and cross-line coordinates, a continuous onedimensional function A(z|xi,yj) may be generated that interpolates theseismic amplitudes associated with the corresponding seismic-trace. Eachone dimensional function A(z|xi,yj) may be transformed, e.g., bycomputing the Hilbert transform of the function A(z|xi,yj), to derive aseries of new functions, for example, referred to as“seismic-attributes” which, for example, together with the functionA(z|xi,yi), may be referred to as a “seismic-properties” functions. Theseismic properties or attributes associated with each cell may bedetermined by sampling the seismic-properties functions at each cell ofseismic cube grid SG. The values of the seismic-properties functions maybe stored with the data for each cell. The seismic properties may becomputed at locations corresponding to the centers or vertices of thecells of seismic cube grid SG and may be stored in the cells of the ofseismic cube grid SG, for example, as another coordinate value. (e.g.,“Gprop”), to generate point coordinates, (x,y,z,Gprop), where Gprop isthe 1D value for the seismic property function. Seismic and/orgeological properties are physical properties associated with thegeological structured being modeled. For example, geological and seismicproperties include porosity, density, geological-time,unwrapped-instantaneous-phase, coherency, impedance, envelop, etc. Otherproperties may be used.

The GeoChron Model and Seismic-Cubes

The following is an example of one process used to generate a GeoChronmodel and a seismic-cube in a computer (other models may be used). Thisprocess (and others herein) may be for example carried out by aprocessor executing code or software instructions. e.g. the system 905shown in FIG. 9:

-   -   1) A network of faults F(t) (e.g., faults 109 of FIG. 1) may be        modeled. e.g., according to mechanisms known in the art.    -   2) A 3D geological domain in G space 104 may be covered by a        mesh, lattice or grid GG including adjacent 3D polyhedral cells.        Reference is made to FIG. 3, which schematically illustrates an        exploded and collapsed or regular view of a geological present        day model 108 in G space 104 having cells 116 in a grid GG 120        according to an embodiment of the invention. Cells 116 are        tetrahedral shape, although any polygonal shape may be used,        e.g., hexahedral. The edges of cells 116 may be tangent to the        surfaces of faults 109 but do not cross these fault surfaces.        The geometry of each cell 116 of grid GG 120 may be defined by        the (x,y,z) coordinates at the vertices of that cell. Since the        uvt-transformation eliminates faults 109 in the depositional        model 110 in G* space 106, the transform functions u(x,y,z),        v(x,y,z) and t(x,y,z) may be discontinuous across faults 109. To        generate these discontinuities, grid GG 120 used to model these        functions may itself be discontinuous, for example as follows:        -   Edges of cells 116 in grid GG 120 may be tangent to fault            surfaces but do not cross these fault surfaces.        -   Collocated vertices of adjacent cells 116 on both sides of a            fault 109 may be duplicated to store distinct location            values u(x,y,z), v(x,y,z) and t(x,y,z) for each cell 116,            e.g., attached at the vertices thereof. Accordingly,            discontinuities of geometric and property functions may be            accurately modeled across faults 109.    -   3) Paleo-geographic coordinates (u,v,t) may be computed. e.g.,        at the vertices of grid GG 120 or at the center or another point        of each cell or voxel in grid 120, e.g., according to mechanisms        known in the art. To generate the paleo-geographic coordinates        (u,v,t), input data may include sets of sampling points {SH(t1),        . . . ,SH(tn)} located on reference horizons {H(t1), . . .        ,H(tn)}, respectively, and extracted from a seismic cube and/or        sampling points observed on well curves (e.g., and referred to        as well markers). Each set of sampling points may be associated        with a depositional horizon {H(t1), . . . ,H(tn)} or level set        across each of which all points in the depositional model have        the same depositional time value, (t1), . . . , (tn),        respectively.    -   4) The paleo-geographic coordinate functions may be generated to        minimize the deformation of each point (x,y,z) or the cumulative        deformation of a subset of points in the current model when they        are transformed to their associated level set horizon {H(t1), .        . . ,H(tn)} for their associated geological time, t_(i), in past        depositional model. The paleo-geographic coordinate functions        u=u(x,y,z), v=v(x,y,z) and t=t(x,y,z) may be fully defined by        their values at the vertices of grid GG 120 or, for example,        other points such as at the center or of each cell in grid GG        120. The value of the paleo-geographic coordinate functions        u(x,y,z), v(x,y,z) and t(x,y,z), may be determined throughout        the geological domain by locally interpolating values of the        functions at each point (x,y,z) from values determined at the        vertices of the cell containing the point (x,y,z). Since the        paleo-geographic coordinate functions define the        uvt-transformation 100, defining the values of the        paleo-geographic coordinate functions (u,v,t) at each vertex of        grid GG 120 may completely define the uvt-transformation 100 at        any point (x,y,z) in G space 104. Different numbers and shapes        of cells 116 or resolutions of grid GG 120 may be used for        different models or different sub-regions within a model. Cells        116 of grid GG 120 may have a resolution or size sufficiently to        detail the variations of the paleo-geographic coordinate        functions and geological time function. The number of cells 116        or resolution of grid GG 120 may, for example, depend on the        “local” or “global” complexity of the horizons and fault network        or discontinuities in the grid. In one embodiment, the number of        cells 116 or resolution of grid GG 120 may be automatically        determined. In another embodiment, the number of cells 116 or        resolution of grid GG 120 may be set, adjusted, or re-calibrated        by a user. In practice, the number of cells of grid GG 120 may        be several orders of magnitude smaller than the number of cells        of a seismic cube grid SG. For example, one hundred thousand        cells 116 of grid GG 120 may be used to cover the same domain as        a seismic cube grid SG including several tens of millions of        cells.    -   5) A 3D geological domain in G* space 106 may be covered by a        mesh, lattice or grid GG* 122. Note that grid GG* 122 may not be        the image of grid GG 120. The grid GG* 122 may define property        values and therefore may be referred to as a “property grid.”        Reference is made to FIG. 4, which schematically illustrates a        uvt transformation 100 from a present day model 108 in G space        104 to a depositional model 110 in G* space 106 according to an        embodiment of the invention. Depositional model 110 may be        covered by a property grid GG* 122. Although property grid GG*        122 is shown in G* space 106, additionally or alternatively, a        property grid may be defined in G space 104, for example,        defining the properties at the vertices of grid GG 120. Property        grid GG* 122 may include adjacent 3D polyhedral cells 124. In a        preferred embodiment, polyhedral cells 124 may be tetrahedral or        hexahedral shaped. Cells 124 of property grid GG* 122 may have a        resolution or size sufficiently to detail the variations of the        seismic properties throughout the model 110. The number of cells        124 or resolution of property grid GG* 122 may be the same or        different as the number of cells 116 or resolution of geometry        grid GG 120. Each cell 124 of property grid GG* 122 may store        one or more seismic and/or geologic property values. In one        example, a single property value may be defined for each cell        124 by the property value of a representative, e.g., center,        point in the cell. In another example, each cell 124 may be        defined by multiple property values. For example, property        values may be collected and averaged at each of multiple points        throughout the cell, e.g., at the vertices or center of edges,        to generate a property average value. The representative or        average property value may be stored at a point in the cell,        e.g., the center point of the cell.    -   6) Property grid GG* 122 may be considered a “texture map” in G*        space 106. The inverse paleo-geographic coordinates x=x(u,v,t),        y=y(u,v,t), and z=z(u,v,t) of the reverse uvt transformation 112        may be used to transport the property values of each cells 124        of property grid GG* 122 from G* space 106 to corresponding        cells 116 of the grid GG 120 in G space 104. The property grid        GG* 122 may be displayed on grid GG 120 by “texture mapping” on        any surface of model 108 in G space 104.    -   7) The 3D geological domain in G space 104 may also be covered        by a seismic cube grid SG. Reference is made to FIG. 5, which        schematically illustrates a uvt transformation 100 from a        seismic cube grid SG 126 of a present day model 108 in G space        104 to a flattened seismic cube grid SG* 128 of a depositional        model 110 in G* space 106 according to an embodiment of the        invention. It may be noted that, contrary to conventional        mechanisms, in some embodiments there are no gaps or overlaps of        points or cells in flattened seismic cube grid SG* 128. Seismic        cube grid SG 126 may be a fine regular mesh or grid including        adjacent 3D polyhedral, preferably hexahedral, cells. Each cell        may store seismic amplitude data collected from seismic signals        and seismic properties derived therefrom. Seismic data or        geological data may be stored, for example, at the vertices or        at the center points of each cell.    -   8) Flattened seismic cube grid SG* 128 in G* space 106 may be        generated as the image of seismic cube grid SG 126 in G space        104 under the uvt-transformation 100. Flattened seismic cube        grid SG 128 SG* may be generated using the uvt-transformation        100, for example, as follows:        -   For each cell SGC of seismic cube grid SG 126 in G space            104, generate the image SGC* of the cell SGC;        -   Store the seismic properties values for each cell SGC of            seismic cube grid SG 126 in G space 104 in each cell 124 of            property grid GG* 122 intersected by the cell SGC.        -   In some embodiments, property grid GG* 122 may include cells            124, which do not correspond to the image of SGC and            therefore, these cells 124 may not be assigned a seismic            property value.    -   9) For each geological-time (t), a faulted/folded level surface        130 in G space 104 may be generated, e.g., using a “marching        mechanism” (e.g., and a marching cube or marching tetrahedral)        known in the art. Each folded or faulted level surface or        horizon 130 in G space 104 may include sets of triangular facets        that correspond to the horizon for that geological-time H(t). A        flattened horizon 132 in G* space 106 may be generated as the        image of the corresponding faulted or folded horizon 130 in G        space 104 under the uvt-transformation 100 from which faults and        folds are removed. Moreover, using 3D-texture mapping operations        known in the art, faulted horizons 130 in G space 104 and        flattened horizons 132 in G* space 106 may be “painted” or        colored with seismic properties, for example, as follows:        -   Seismic cube grid SG 126 may be used as a “3D-texture            domain,” to paint faulted horizons H(t) 130 in G space 104            with seismic properties, the coordinates (x,y,z) of the            vertices of the triangular facets of faulted horizons H(t)            130 may be used as “texture-coordinates” referring to the            seismic grid 126. That is, seismic property values may be            defined at the vertices of the triangular facets of faulted            horizons H(t) 130 in G space 104. For example, a user may            select a property or property values and select the points            (e.g., cell SGC vertices or centers), horizons, or regions            of seismic cube grid SG 126 to which those values are            assigned. The assigned values are then stored at the texture            coordinates. The user may select these points using, e.g.,            input device 965 of FIG. 9 such as a mouse, trackball,            and/or keyboard. User input may alter the visualization of            these points or regions, e.g., on a computer screen, such as            display 980 of FIG. 9.        -   To paint flattened horizons H*(t) 132 in G* space 106 with            seismic properties, the coordinates            {x(u,v,t),y(u,v,t).z(u,v,t)} of the reverse uvt-transform            112 in G space 104 of vertices of the triangular facets of            flattened horizons H*(t) 132 in G* space 106 may be used as            “texture-coordinates.” Seismic cube grid SG* 128 may be used            as a “3D-texture domain,” to paint flattened horizons H*(t)            132 in G* space 106 with seismic properties. That is, the            property values assigned to texture coordinates of seismic            cube grid SG 126 in G space 104 may be assigned to            corresponding texture coordinates of flattened seismic cube            grid SG* 128 in G* space 106.        -   Representations of faulted horizons H(t) 130 and/or seismic            cube grid SG 126 in G space 104 and/or flattened horizons            H*(t) 132 and/or seismic cube grid SG* 128 in G* space 106            may be displayed to a user on a monitor, e.g., display 980            of FIG. 9.        -   Although the above describes first painting properties on            horizons in G space 104 and then transforming those            properties to G* space 106 using the forward            uvt-transformation 100, embodiments of the invention may            similarly include first painting properties on horizons in            G* space 106 and then transforming those properties to G            space 104 using the reverse uvt-transformation 112.        -   Painting or assigning property values to vertices, cells or            facets changes the data associated with modeled points. For            example, when a coordinate (x,y,z) is painted with a            property p0, the coordinate is transformed to (x,y,z,p0).            Thus, the physical data of a geophysical subsurface            structure, e.g., a particle of sediment, represented by the            painted coordinates is altered.    -   10) STOP

In some embodiments, vertices of each cell 116 of grid GG 120 may storeboth (x,y,z) coordinates and (u,v,t) coordinates. Accordingly, cells 116of grid GG 120 may be simultaneously defined in G space 104 by their(x,y,z) coordinates and in G* space 106 by their (u,v,t) coordinates,i.e., the uvt-transformation of their (x,y,z) coordinates.

In FIG. 5, due to the discontinuities across faults 109 of seismic cubegrid SG 126 and the discontinuous uvt-transformation 100 required toremove those faults, the image of the (e.g., cubic) shaped seismic cubegrid SG 126. i.e., flattened seismic cube grid SG* 128, may be deformed(e.g., to not be a cube shape). This may result from the property thatIPG-lines described herein may be non-vertical lines and arediscontinuous across faults 109. An advantage of such embodiments overconventional mechanisms, is that flattened seismic cube grid SG* 128 maybe accurately modeled, (without holes or duplicate points) even in thepresence of non-vertical faults (normal or reverse faults) crossing inthe vertical direction.

Furthermore, seismic cube grid SG 126 may be coherent with the GeoChronmodel such that, for example, for each geological-time (t), seismicproperty values may be approximately constant along the correspondingfaulted horizon H(t) 130 in G space 104 and, similarly, along thecorresponding flattened horizon H*(t) 132 in G* space 106. When seismicproperty values are not constant in a region of faulted horizon H(t) 130or its image, flattened horizon H*(t) 132, the following cases may beconsidered:

-   -   1. In a first case, the original GeoChron model 108 stored using        grid GG 120 may be locally inconsistent with the seismic cube        grid SG 126 generated therefrom. In such a case, the local        region where such inconsistencies occur may be marked as a        region of error, for example, denoted by EH(t) in G space 104        and EH*(t) in G* space 106 and may require locally changing or        updating the uvt-transformation 100.    -   2. In a second case, the non-constant seismic property values        may represent a real situation in which a horizon has geometric        continuity (i.e., it is not cut or folded by faults, erosion or        other geometric changes) but the horizon has discontinuities in        properties (e.g., sedimentary structures deposited at the same        geological-time (t) have different properties). Examples of such        sedimentary structures or “geobodies” include channels, lenses        and dunes, which are locally discontinuous in property values        but not in geometry. In such a case, the non-constant behavior        of the seismic properties is accurate and should not be locally        changed in these geobodies.        Geological-Time-Volume

Among the many seismic properties which may be derived from seismicamplitudes in a seismic cube grid SG, the property referred to as“unwrapped-instantaneous-phase” may attempt to model geological time.For each vertical seismic-trace corresponding to a given pair {xi,yj} ofin-line and cross-line coordinates, the 1 D seismic-amplitude functionA(z|xi,yj) may be transformed into a new 1D function, IP(z|xi,yj),referred to as the “instantaneous phase” function. The instantaneousphase function, IP(z|xi,yj), may vary, e.g., periodically, with (z).Using “unwrapping” methods known in the art, the instantaneous phasefunction, IP(z|xi,yj), may be transformed to a non-periodic monotonicfunction UIP(z|xi,yj). The unwrapped instantaneous phase function may bemay attempt to model a geologic-time function. The values of thegeological-time function (i.e., the unwrapped instantaneous phasefunction UIP(z|xi,yj)) may be sampled and stored in the cells of thesame seismic cube grid SG containing the seismic amplitude. A seismiccube grid SG storing geological-time values for the cells may bereferred to as a “Geological-Time-Volume” (GTV). However, thegeological-time-volume generated using the unwrapped instantaneous phasefunction has many limitations, as described herein.

GeoChron Model Versus Geological-Time-Volume

For the sake of clarity, differences and similarities betweenembodiments of the invention, e.g., using the GeoChron model andconventional mechanisms using the geological-time-volume (GTV) aredescribed.

-   -   Computation of geological time:        -   In the GTV approach, geological-time is deduced directly            from the seismic amplitudes. Therefore, a seismic cube grid            SG must be given as input data to compute the geological            time. The geological-time is identified with an unwrapped            seismic phase and is computed in 1D along seismic traces. It            may be appreciated that discontinuities (e.g., faults and            unconformities) are not modeled beforehand and are generally            deduced from the GTV.    -   According to embodiments of the inventions, e.g., in the        GeoChron approach, geological-time of a 3D model may be        interpolated in 3D for example as a piecewise continuous        function. To generate the geological-time, sampling points,        e.g., irregularly sampled sets of points {SH(t1), . . .        ,SH(tn)}, may be used as input data and arbitrary increasing        geological times may be assigned thereto. These sets of sampling        points may be extracted from seismic cubes, e.g., using        auto-picking mechanisms and/or may be points at the intersection        of well paths and horizons referred to as “well-markers”. When        sampling points only include well-markers, geological-times may        be computed independently of seismic data, but using        discontinuity data (e.g., data associated with faults and        unconformities). With the GTV approach, well markers        corresponding to the crossing of well curves with horizons        typically cannot be taken into account.    -   In contrast with the geological times used in the GTV approach,        embodiments of the present invention based on the        uvt-transformation typically do not directly use or even may not        use at all seismic cube data to generate geological times, while        the GTV model does. However, when seismic data is not used,        embodiments of the present invention may use fault data, while        the GTV model typically does not.    -   Furthermore, the GTV approach relies on the        unwrapped-instantaneous-phase technique and on 1D interpolations        in the vertical direction while embodiments of the present        invention may use a full 3D interpolation mechanism, such as,        for example, a Discrete-Smooth-Interpolation (DSI) mechanism.    -   Storage of the geological-time:

In the GTV approach, similarly to the seismic amplitude values,geological-time values are stored in each cell of the seismic cube gridSG. Seismic cube grids SG typically include regular structured 3D cellswith the same cubic shape and size. Such seismic cube grids SG typicallycontain tens of millions of cells and may contain as many as hundreds ofmillions of cells. Accordingly, tens to hundreds of millions ofgeological time values may be stored in the GVT approach, imposing agreat computational burden for the storage and usage of thegeological-time data.

In contrast, in embodiments of the present invention, geological-timevalues may be stored at the vertices of an unstructured grid GG havingpolyhedral cells that may vary in shape and size, where the edges do notcut discontinuities (e.g., faults and unconformities). Generally, only afew hundreds of thousands of cells and geological time values (e.g.,associated with the vertices of these cells) may be used to generate anaccurate geological-time model.

Accordingly, compared to the GTV approach, embodiments of the presentinvention use significantly less storage space for geological-time data,e.g., storing a factor of a hundred to a thousand times fewergeological-time values.

-   -   Extracted horizon:

In the GTV approach, a horizon includes a set of points located along aseismic trace that have the same geological time (t). For eachseismic-trace whose cells have the same (x,y) coordinates, a 1D searchis used to retrieve the one or more cells with the same geological-time(t). The horizon corresponding to the geological time (t) includes a setof points SH(t) whose projections on the (x,y) plane is a regular 2Darray. The number of such points in SH(t) is proportional to the size ornumber of cells of the seismic cube grid SG in the (x) and (y)directions.

According to embodiments of the invention, e.g., in the GeoChronapproach, for each given geological-time (t), a corresponding horizonH(t) includes a set of, e.g., triangular, facets extracted in 3D fromthe irregular grid GG (e.g., using a known marching-tetrahedra method).The number of triangular facets of a horizon H(t) may be proportional tothe number of cells of the irregular grid GG, e.g., only a few hundredsof thousands of cells.

For storing a horizon, the GTV approach uses a number of data pointscorresponding to the number of cells in the seismic cube grid SG (e.g.,tens of millions), while embodiments of the invention may use a numberof data points corresponding to the number of cells in an irregular gridGG (e.g., thousands). Therefore, compared to the GTV approach,embodiments of the present invention use significantly less space forstoring horizons.

Furthermore, in the GTV approach, a horizon is modeled by a set ofpoints, while in embodiments of the invention, e.g., in the GeoChronapproach, a horizon is modeled by a set of polygons. e.g., triangles.Each polygon may be a local approximation of a mean value surface thatconnects a set of points therein. Representing a horizon by polygonsinstead of points allows a surface to be modeled using fewer points(e.g., when a triangle is used, the coordinates of the three verticesmay be sufficient to fully-define the geometry of the triangleregardless of size). A more compact representation may be achieved usingpolygons as opposed to points.

-   -   Flattening a seismic cube:

In the GTV approach, since IPG lines extend only in the verticaldirection, flattening a seismic cube may also be restricted to movingthe cells of the seismic cube grid SG in the vertical direction. Sincefaults in the subsurface are predominantly non-vertical, a strictlyvertical motion cannot generate an accurate reversal of the faultsrequired to generate an accurate depositional model.

According to embodiments of the invention, e.g., in the GeoChronapproach, a seismic cube may be flattened according to auvt-transformation or another global geological-time transformation, inwhich cells of the seismic cube grid SG may be moved in all of the 3Ddirections along the curvilinear IPG-lines.

In conclusion, although similar names, for example, “geological-time” or“horizons”, are used to refer to structures in the GTV approach and inembodiments of the present invention, these structures are quitedifferent. In practice, geological-time values in the GTV approach andin embodiments of the present invention have different values. In somecases, the output of GTV approach may be considered as input forbuilding a uvt-transformation:

-   -   a) The set of points {SH(t1), . . . , SH(tn)} corresponding to        the horizons of the GTV approach may be used as input data in        the GeoChron to interpolate the (GeoChron)-geological-time in        3D.    -   b) The discontinuities corresponding to faults and        unconformities may be directly extracted from a GTV and then        used as input by the GeoChron model to interpolate in 3D the        (GeoChron)-geological-time.

While the GTV model is imperfect, embodiments of the invention may beused in combination therewith.

For simplicity and clarity of illustration, embodiments of the inventionare described in two sections (elements from each may of course becombined in some embodiments).

-   -   The first section, entitled “Incremental construction of a        GeoChron model from a seismic-cube”, describes mechanisms which        may be used according to embodiments of the present invention to        incrementally define and alter or update the present day model        and depositional model, for example, by locally changing the        functions u(x,y,z), v(x,y,z), and t(x,y,z) that define the        uvt-transformation. A user may control the incremental change        using an interactive user interface.    -   The second section, entitled “Extraction of geo-bodies from a        seismic-cube and a GeoChron model” describes mechanisms which        may be used according to embodiments of the present invention to        alter the present day model and depositional model,        simultaneously, by adding or changing geophysical properties        assigned to the model. In one embodiment, geobodies may be        identified and used to build a property model associated with        the present day and depositional models.

Incremental Construction of a Dual Model Relating a Present DayStructures and Past Depositional Structures

Incremental Construction of a Dual Model from a Seismic Cube

Processor 940 of FIG. 9 may determine or receive an indication of, e.g.,from a user operating an input device, points to be edited, altered orremoved from faulted horizon 130 in G space 104 or flattened horizon 132in G* space 106. For example, faulted or flattened horizon 130 or 132may be displayed on display 980, which a user may inspect to select ormark points in one of the horizons to be edited, e.g., using inputdevice 965. Processor 940 may edit the marked horizon and mayautomatically, and preferably simultaneously may edit the otherun-marked horizon in a corresponding manner.

As described in the section entitled, “The GeoChron Model andSeismic-Cubes”:

-   -   in step 3 of one example process, to generate the        paleo-geographic coordinates (u,v,t), input data may include        sets of sampling points {SH(t1), . . . ,SH(tn)} located on        reference horizons {H(t1), . . . ,H(tn)} and extracted from a        seismic cube grid SG 126; and    -   The image of a faulted or folded horizon 130 of seismic cube        grid SG 126 in G space 104 under uvt-transformation 100 may be a        flattened horizon 132 of flattened seismic cube grid SG* 128 in        G* space 106 such that flattened horizon 132 may be flat (e.g.,        having a constant value range in the geological-time axis t) and        any faults 109 intersecting faulted horizon 130 are removed        (e.g., as shown in FIGS. 1, 5, 7, and 8).

Using these features, embodiments of the invention provide a mechanismto incrementally generate models, for example, a dual model such as theGeoChron model, as follows. This process (and others herein) may be forexample carried out by a processor executing code or softwareinstructions, e.g. the system 905 shown in FIG. 9:

-   -   1) A network of faults F(t) (e.g., faults 109 of FIG. 1) may be        modeled.    -   2) A 3D geological domain in G space 104 may be covered by a        mesh, lattice or grid GG 120 including adjacent 3D polyhedral        cells 116, e.g., as shown in FIG. 3. Polyhedral cells 116 may        be, for example, tetrahedral shaped (as in FIG. 3) or hexahedral        shaped, or may be other suitable shapes. The edges of cells 116        may be tangent to the surfaces of faults 109 but do not cross        these fault surfaces. The geometry of each cell 116 of grid GG        120 may be defined by the (x,y,z) coordinates at the vertices of        that cell. Since a uvt-transformation 100 eliminates faults 109        in the depositional model 110 in G* space 106, the transform        functions u(x,y,z), v(x,y,z) and t(x,y,z) may be discontinuous        across faults 109. To generate these discontinuity, grid GG 120        used to model these functions may itself be discontinuous across        faults, for example as follows:        -   Edges of cells 116 in grid GG 120 may be tangent to fault            surfaces but do not cross these fault surfaces.        -   Collocated vertices of adjacent cells 116 on both sides of a            fault 109 may be duplicated to store distinct location            values for each cell 116, e.g., attached at the vertices            thereof. Accordingly, discontinuities of geometric and            seismic property functions may be accurately modeled across            faults 109.    -   3) The 3D geological domain in G space 104 may also be covered        by a seismic-cube grid SG 126, for example, as shown in FIG. 5.        Seismic cube grid SG 126 may be a fine regular mesh including        adjacent 3D polyhedral, preferably hexahedral cells. Each cell        may store for example seismic amplitude data collected from        seismic signals and seismic properties derived therefrom.    -   4) A 3D geological domain in G* space 106 may be covered by a        mesh, lattice or grid GG* 122. Grid GG* 122 may store seismic        and/or geological property values and therefore may be referred        to as a “property model.” Property grid GG* 122 may include        adjacent 3D polyhedral cells 124 preferably having a hexahedral        shape (e.g., as shown in FIGS. 4 and 8). Cells 124 may have a        resolution or size sufficiently to detail the variations of the        seismic and/or geological properties throughout the depositional        model 110. A user may paint or assign property values to model        110, e.g., using an input device such as a mouse and/or        keyboard, which are defined at the cells of property grid GG*        122. Using the reverse uvt-transformation 112 the new property        values may be automatically assigned to the corresponding cells        of seismic property grid GG 120 in G space 104 and displayed on        model 108 (e.g., as shown in FIG. 3).    -   5) Select an initial subset of reference horizons RH={H(t1), . .        . ,H(tn)} in G space 104. Any reference horizons may be used,        for example, the most visible and simple to interpret horizons        in the seismic cube grid SG 126 as determined by a user. The        number, n, of reference horizons in the initial subset may be        small. For example, two reference horizons may be selected,        e.g., located in the neighborhood of the bottom and top parts of        the 3D geological domain in G space 104.    -   6) For each horizon H(ti) of the selected subset of reference        horizons RH, a user may select “seed points” SP(ti)={p1,p2, . .        . } on the horizon in G space 104. The points may be selected        from a corresponding vertical cross sections of seismic cube        grid SG 126 in G space 104. For example, the user may click or        press a button or key on a mouse (or any other input device) to        select these points.    -   7) For each horizon H(ti) of the selected subset of reference        horizons RH, use the seed points SP(ti) to extract a subset        SH(ti) of sampling points located on the horizon in G space 104.        If well markers corresponding to the intersections of well        curves with H(ti) are given, then these well markers may be        added to SH(ti).    -   8) Define SH to be the set of all the subsets of extracted        sampling points, for example, as follows:        SH={SH(t1), . . . ,SH(tn)}.    -   9) Using input data SH, compute the geological-time function        t(x,y,z) of the GeoChron model e.g., according to a mechanism        known in the art, and such that the geological-time function        t(x,y,z) is approximately equal to (ti) for any location (x,y,z)        of a sampling point in SH(ti).    -   10) Using the geological-time function t(x,y,z), compute the        paleo-geographic coordinate functions u(x,y,z) and v(x,y,z),        e.g., according to a mechanism known in the art. Accordingly,        since the geological-time function t(x,y,z) and the        paleo-geographic coordinate functions u(x,y,z) and v(x,y,z) are        now defined, the uvt transformation 100 is defined.    -   11) Using the uvt-transformation, a flattened seismic cube grid        SG* 128 in G* space 106 may be generated as the image of seismic        cube grid SG 126 in G space 104 under the uvt-transformation 100        (e.g., as shown in FIG. 5).    -   12) Initialize a region QC* to be an empty subset of G* space        106. The region QC* may include a subset of points of model 110        and may be a local region of the geological domain in G* space        106 where the GeoChron model may be locally altered, updated or        changed.    -   13) Control the quality of the GeoChron model by adding regions        of the G* space 106 to the empty set QC* where the GeoChron        model is to be improved or updated, for example, as follows:        -   (a) Control the visual quality of cross-sections of            flattened seismic cube grid SG* 128 in G* space 106. For            example, for each vertical cross-section of the flattened            seismic cube grid SG* 128 in G* space 106: If the GeoChron            model is accurate, then, local irregularities or            heterogeneities induced for example by sedimentary            structures such as lenses, channels or dunes, are accepted            then the extrema of the seismic property values on these            cross sections should appear to be horizontally aligned.            Otherwise, if there are regions in G* space 106 of these            cross sections where the extrema of the seismic property            values are not horizontally aligned, e.g., as determined by            visual inspection by a user, then the user may select these            regions to be added to QC*. For example, individual points,            lines, triangles, polygons, polyhedra or other surfaces may            be added to the region QC*.        -   (b) Control the visual quality of the flattened horizons            H*(ti) 132 at geological-times (ti) of flattened seismic            cube grid SG* 128 in G* space 106. For example, for each            flattened horizon H*(ti) 132 of the flattened seismic cube            grid SG* 128 in G* space 106: If the GeoChron model is            accurate, then the seismic property values in seismic cube            grid SG* 128 are approximately constant for each flattened            horizon 132. Otherwise, if there are regions of the            flattened horizons H*(ti) 132 where the seismic property            values are not approximately constant, e.g., as determined            by visual inspection by a user, then the user may select            these regions or subset of points to be added to QC*.        -   (c) Control the numerical quality of cross-sections and/or            horizons H*(ti) 132 at geological-times (ti) of flattened            seismic cube grid SG* 128 in G* space 106. A user or            programmer may select a standard deviation threshold to be            programmed in a computing device. For example, for each            cross-section and/or flattened horizon H*(ti) 132 of            flattened seismic cube grid SG* 128 in G* space 106: the            computing device may determine the standard deviation            threshold of the seismic property values thereof. If the            GeoChron model is accurate, then the standard deviations for            each cross-section and/or flattened horizon H*(t) may be            approximately zero. Otherwise, if the standard deviation            threshold is greater than or equal to the programmed            standard deviation threshold in one or more regions or            points of the cross-sections and/or flattened horizons H*(t)            132, add these regions or points, e.g., or any region of GG*            where the standard deviation is above the programmed            threshold, to QC*.    -   14) If QC* is not an empty set, then:        -   (a) The inverse uvt-transformation QC of the region QC* may            be computed and then all extracted sampling points SH            contained in QC may be removed from SH.        -   (b) A series of “seed points” SP*(tnew)={p*1,p*2, . . . } in            G* space 106 may be selected which are located at the            intersection of QC* with a horizon H*(tnew), e.g., selected            by a user. For example, the user may select the seed points            by clicking (e.g., pressing or clicking on an input device            which controls an on-screen cursor, indicator, button or            other tool) on the visualization of the points in G* space            106 or their reverse uvt-transformation points in G space            104 using a mouse or another input device.        -   (c) A series of seed points SP(tnew)={p1,p2, . . . } located            in G space 104 may be generated by transforming the series            of seed points SP*(tnew)={p*1,p*2, . . . } in G* space 106            using the current reverse uvt-transformation 112. That is,            for each point p* of the series of seed points SP*(tnew) in            G* space 106, the point p of the series of seed points            SP(tnew) in G space 104 is the reverse uvt-transformation of            the point p*.        -   (d) A subset SH(tnew) of sampling points located on the            horizon H(tnew) may be automatically extracted using the            series of seed points SP(tnew) in G space 104 and the            current geological-time function t(x,y,z). For example, the            sampling points may be extracted according to the series of            operations described in the section entitled, “Using the            geological-time function t(x,y,z) to extract sampling points            on horizons.”        -   (e) The subset SH(tnew) of sampling points located on the            horizon H(tnew) may be added to the set of all extracted            sampling points SH and the corresponding horizon H(tnew) may            be added to the set of reference horizons RH.        -   (f) Repeat steps (14.b) to (14.e) using a new value (tnew)            of the geological-time function corresponding to a horizon            H*(tnew) visible in the set QC*.        -   (g) Proceed to step (9) to update and locally change the            geological-time function t(x,y,z) to include local changes            of the new set of sampling points. The process may proceed            to step (10) to generate the corresponding locally edited            paleo-geographic coordinate functions u(x,y,z) and v(x,y,z).            Together the independently locally edited functions            u(x,y,z), v(x,y,z), and t(x,y,z), form the 3D            uvt-transformation locally edited in three dimensions. Steps            (9)-(14) may be iteratively repeated, for example, to            incrementally generate a new locally edited version of the            uvt-transformation.    -   15) STOP

Other operations or series of operations may be used.

It may be noted, at step 14-g of the above process, returning to step(9) allows an incremental construction of a dual model from data storedin seismic cubes (e.g., in seismic cube grid SG 126 in G space 104 orflattened seismic cube grid SG* 128 in G* space 106).

An error in the GeoChron model may exist for example when a point in Gspace 104 is assigned the wrong geological-time (t) and is therebymapped to the wrong horizon H*(t) in G* space 106 usinguvt-transformation 100. Since seismic-property values are ideallyconstant on horizons in G space 104 and horizontal cross sections in G*space 106, such an erroneous point may be detected, for example, by auser inspecting a visualization of the property values of flattenedseismic cube grid SG* 128 in G* space 106 to identify any stray pointsdeviating from the ideally constant property values or by a computingdevice identifying any greater than threshold standard deviations acrossthe horizons or horizontal cross sections. Since geobody structurescause discontinuities in seismic property values that are accurate, anydeviations in seismic property values attributed to geobodies are noterroneous and may therefore be ignored when correcting the model. Aprocessor 940 of FIG. 9 may receive the user selected points to beedited, altered or removed, e.g., via commands from user input device965 of FIG. 9, mouse click commands (or other suitable input) indicatingthe undesired points.

Alternatively, a processor, e.g., processor 940 of FIG. 9, mayautomatically identify any problematic points or points to be changed bymeasuring the standard deviation of property values on horizons in Gspace 104 or horizontal cross sections in G* space 106. When theprocessor measures standard deviation values for a property that isgreater than a predetermined threshold in a local region (e.g., aneighborhood of a point), the processor may automatically identify thedeviating point or points and may select the point to be changed andcorrected.

Once the sampling points to be changed are identified, in someembodiments, a new point may be selected to replace the changed point.Accordingly, in one embodiment, a new seed point may be selected that islocated in the neighborhood of the erroneous point and a correctflattened horizon 132. The new point may be selected that has seismicproperty values consistent with those throughout the correct flattenedhorizon 132 (e.g., with a standard deviation of approximately zero) toensure that the new point is not itself an erroneous point. Correctflattened horizon 132 may be a pre-existing horizon or may be generated,e.g., using an auto-picking mechanism. A corresponding new samplingpoint may be generated in G space 104. The new sampling point in G space104 may be the reverse uvt-transformation 112 of the new sampling pointin G* space 106.

Faulted and folded horizon 130 and flattened horizon 132 may be alteredsuch that the erroneous points of depositional model 110 may be replacedin G* space 106 with a new point located on a flattened horizon 132.e.g., selected by a user, and the point corresponding to the reverseuvt-transformation 112 of the erroneous point in present day model 108may be replaced in G space 104 with the point located on the faultedhorizon 130 corresponding to the reverse uvt-transformation 112 of thenew point located on a flattened horizon 132, e.g., determinedautomatically by a processor. Other additional points may also be addedto G space 104 and/or G* space 106 in a neighborhood or seismic windowof the new points, as described in the section entitled, “Using thegeological-time function t(x,y,z) to extract sampling points onhorizons”.

To alter, update or locally change the GeoChron model accordingly,uvt-transformation 100 may be locally changed or refined to take intoaccount the removal of the erroneous points QC* in G* space 106 andtheir corresponding points QC in G space 104 and to take into accountnew sampling points in G* space 106 and their corresponding points in Gspace 104. For example, to refine the GeoChron model uvt-transformation100 may be globally left unchanged, but may be locally changed, toreplace the points of error with new corrected points. For example, theuvt-transformation 100 may be locally updated or changed byre-interpolating the uvt-transformation 100 using added, deleted, ormoved sampling points as local constraints in a DSI Interpolationmethod.

In some embodiments, changing the global transformation for the subsetof points to a “local transformation” locally changes or edits theglobal transformation at those points (e.g., and in the neighborhood ofthose points to generate a smooth local function).

In an embodiment of the invention, a computing system or processor maymodel a subsurface structure at a time period when the structure wasoriginally formed. A memory or other device may store a first modelhaving a plurality of non-planar horizons representing a current stateof the subsurface structure. One or more processors may compute anon-uniform vector field, e.g. {u(x,y,z), v(x,y,z), t(x,y,z)}, based onthe non-planar geometry of the horizons of the first model. Using thenon-uniform vector field. e.g., a three-dimensional (3D) vector field,the processor may transform geographic coordinates (x,y,z) of the firstmodel to depositional coordinates of a second model (u,v,t) representinga predicted or possible state of the subsurface structure at a pastgeological time when the subsurface structure was originally deposited:such a transformation may be referred to as a uvt-transformation or auvt-transform. A user or auto-picking algorithm may select a finite setof sampling points in the first model associated with the same horizonH(t_(i)) in the second model. A set of points associated with the samehorizon H(t_(i)) in the past depositional model may have the samegeological time (t_(i)) of deposition. The processor may flatten thesepoints associated with the same horizon from a non-planar subset ofpoints in the first model to a horizontal plane or level set in thesecond depositional model. e.g., associated with a constant value of thegeological time (t). The processor may generate correspondingpaleo-geographic coordinates (u,v) for each point so that theuvt-transformation minimizes the deformation of the subsurface structurefrom the past depositional model to the current model. Theuvt-transformation may define each of the paleo-geographic coordinates(u,v) to be least squares solutions to a plurality of deformationequations. The geological time coordinate (t) may contribute aone-dimensional transformation to the (x,y,z) points of the present daymodel and the paleo-geographic coordinates (u,v) may contribute anadditional two-dimensional transformation to the (x,y,z) points of thepresent day model, generating a total of three-dimensional (3D)uvt-transformation between the 3D present day model 108 and 3Ddepositional model 110. That is, each point (u,v,t) of G* space 106 notbelonging to an eroded region may be transformed into a point (x,y,z) ofG space 104 with three degrees of freedom (e.g., where at least somepoints are moved in a direction that is the vector sum of threerespectively perpendicular directions).

The forward uvt transformation 100 may map a finite set of (x,y,z)points in the present day model 108 to a finite set of (u,v,t) points inthe depositional model 110 (e.g., using a one-to-one correspondence).The finite sets of points in the present day model 108 may be, forexample, defined as the set of nodes of a 3D mesh or grid 120 or atother points, such as the vertices or center points of voxels composinga 3D grid in G space 104. Inside each cell 116 of the 3D grid 120 in Gspace 104, the processor may then locally interpolate the transformation“between the nodes” to transform any point (x,y,z) in G space 104 into apoint (u,v,t) in G* space 106 using the forward uvt transformation 100and any point (u,v,t) in G* space 106 to any point (x,y,z) in G space104 using the reverse uvt transformation 112.

When a change in either the past depositional model 110 or the currentmodel 108 is made, the current uvt-transformation 100 or 112 may nolonger minimize the deformations of the terrains between the pastdepositional model and the present day model. The processor may thenre-compute or re-interpolate the uvt-transformation between the currentand depositional models to generate an updated uvt-transformation thatincorporates the local changes (e.g., the moved, deleted, added pointsin either model), while still minimizing the deformations of theterrains between the models. The re-computation may locally or globallychange or update the initial uvt-transformation to incorporate new orchanged positions of new or changed sampling points, e.g., so thatlocally changed points in the current model associated with the samedepositional horizon are continuously transformed to the same planardepositional horizon of the depositional model with no gaps and nooverlaps.

These local changes represent deformations of pieces of sediment thatover time have moved in a path with a greater than minimal deformation.Although less likely, such deformations do occur in nature and may berecognized by a user and entered manually to locally change theautomated model which otherwise automatically generates minimaldeformations.

Paleo-geographic coordinates, e.g., u(x,y,z) and v(x,y,z), may begenerated according to, for example, embodiments of the inventiondescribed in U.S. patent application Ser. No. 12/791,352, issued as U.S.Pat. No. 8,711,140, which is incorporated by reference herein in itsentirety. Other methods of generating paleo-geographic coordinates maybe used.

Geological time function, e.g., t(x,y,z), may be generated according to,for example, embodiments of the invention described in U.S. patentapplication Ser. No. 12/791,370, issued as U.S. Pat. No. 8,600,708 whichis incorporated by reference herein in its entirety. Other methods ofgenerating a geological-time function may be used.

It is contemplated that modifications and combinations of this series ofoperations will be readily appreciated by those skilled in the art andare within the spirit and scope of the invention.

Using the Geological-Time Function t(x,y,z) to Extract Sampling Pointson Horizons

In the series of operations described in the section entitled,“incremental construction of a GeoChron model from a seismic cube,” newpoints in G space 104 may be defined using the reverse uvttransformation to replace erroneous points in G* space 106. However,considering the large volume of data points typically associated withgeological models, individually deleting and adding points may be adifficult and laborious task. Accordingly, embodiments of the inventionprovide a mechanism for automatically extracting a set of new samplingpoints SH(tnew) in G space 104 for each new point added in G space 104to locally change the uvt-transformation therebetween.

Reference is made to FIG. 6, which schematically illustrates a seismicwindow W(x,y,z) 134 centered on a new point (x,y,z) of seismic cube gridSG 126 in G space 104 used to automatically generate additional pointsto add to model 108 according to an embodiment of the invention. Centerpoint (x,y,z) and seismic window W(x,y,z) 134 may be selected by a user,e.g., via input device 965, or automatically, e.g., by processor 940 ofFIG. 9. Seismic window W(x,y,z) 134 may be displayed on display 980.Seismic window W(x,y,z) 134 may be, for example, a small 3D hexahedralbox centered at a point (x,y,z) in the seismic cube grid SG 126 andcorresponding to the seismic signal along one or more vertical traces136 of a seismic property. Vertical traces 136 may for example intersectthe (x,y) plane with vertical coordinates (e.g., representing altitudeor seismic-time) in a range of [z−T1,z+T2], where T1 and T2 may beautomatically determined or selected by a user. For example, if (z)represents seismic-time, then T1=T2=30 milliseconds. Other time valuesmay be used.

The point (x,y,z) may be a newly added point generated in step 14(c) ofthe section entitled “incremental construction of a GeoChron model froma seismic cube.” The set of new sampling points SH(tnew) in step 14(d)of the section entitled “incremental construction of a GeoChron modelfrom a seismic cube” may be generated, for example, as follows:

In a first embodiment, for a given seed point or a sampling point (s0)extracted. e.g., by a user, from H(tnew) having coordinates (x0,y0,z0)in the G space 104, a new sampling point (s) may be selected, e.g., by auser via user input device 965 of FIG. 9, in the neighborhood of (s0) tobe added to SH(tnew), for example, as follows:

-   -   1. Intervals or step sizes sx and sy may be selected in the x        and y directions, respectively, of seismic cube grid SG 126.    -   2. A point (q) neighboring (s0) with coordinates (x0+sx, y0+sy,        z0) may be selected, e.g., by a user via user input device 965        of FIG. 9.    -   3. Seismic windows W(x0,y0,z0) and W(x0+sx, y0+sy, z0) may be        extracted from the seismic cube grid SG 126, e.g., automatically        by processor 940 of FIG. 9.    -   4. The seismic window W(x0,y0,z0) of point s0 may be compared to        the seismic window W(x0+sx, y0+sy, z0) of point (q) to determine        the optimal value of (dz) such that (s) with coordinates        (x0+sx,y0+sy,z0+dz) best correlates with (s0), e.g., determined        by processor 940 of FIG. 9, according to a correlation function.        For example, a correlation function may be a mathematical        function comparing the values stored in seismic windows        W(x0,y0,z0) and W(x0+sx, y0+sy, z0) to determine one or more        points (x0+sx,y0+sy,z0) therein having a minimum difference in        seismic property values, location or other parameters from the        center point (x0,y0,z0).    -   5. Add (s) to the refined set of sampling points SH(tnew).    -   6. STOP

Other operations or series of operations may be used.

In a second embodiment, for a given seed point or a sampling point (s0)extracted from SH(tnew) having coordinates (x0,y0,z0) in the G space104, a new sampling point (s) may be selected, e.g., in the neighborhoodof (s0) to be added to SH(tnew), taking into account the currentgeological-time function t(x,y,z), for example, as follows:

-   -   1. Intervals or step sizes sx and sy may be selected in the x        and y directions, respectively, of seismic cube grid SG 126.    -   2. A value (znew) may be determined so that t(x0+sx, y0+sy,        znew) is equal to (tnew).    -   3. Seismic windows W(x0,y0,z0) and W(x0+sx, y0+sy, znew) may be        extracted from the seismic cube grid SG 126.    -   4. The seismic window W(x0,y0,z0) of point s0 may be compared to        the seismic window W(x0+sx, y0+sy, znew) to determine the        optimal value of (dz) such that the point (s) with coordinates        (x0+sx,y0+sy,znew+dz) best correlates with (s0).    -   5. Add (s) to the refined set of sampling points SH(tnew).    -   6. STOP

Other operations or series of operations may be used. An auto-pickingmechanism may automatically select points that correlate with the newpoints based on a correlation function, e.g., minimizing a standarddeviation of property values. Additional sampling points added in Gspace 104 may be located in a neighborhood. e.g., a seismic window, ofsome or all point(s) newly added in step 14(c) of the section entitled“incremental construction of a GeoChron model from a seismic cube.”

In the first embodiment, the neighborhood or a seismic window forpicking points may be generated based on the position of vertical traces136 and the range of the vertical coordinate (z). e.g., [z−T1,z+T2] inthe example above. It may be noted that, in G space 104, the verticalcoordinate (z) may for example represent seismic altitude orseismic-time, but does not represent the geological-time t(x,y,z). Aseismic signal may represent a record of a seismic wavelet along aseismic-time at a given location. Since a seismic wavelet takes moretime to travel the deeper it goes below the subsurface, seismic-time maycorrespond to the depth of subsurface geologic structures.

In the second embodiment, the neighborhood or a seismic window forpicking sampling points on a horizon may be generated based on thegeological-time t(x,y,z) (e.g., see steps 2, and 3.). Since thegeological-time function t(x,y,z) is discontinuous across faults, e.g.,jumping across faults to link geometrically disconnected points on bothsides of a fault, a seismic window generated using the geological-timefunction t(x,y,z) allows the window to “jump” or extend across fault aswell. Accordingly, if points (s) and (s0) are on opposite sides of afault, point (s) may still be in the window of point (s0) if they have asimilar geological-time (t). Thus, points (s) across a fault may becorrectly linked and correlated with point (s0) when they meet asufficient correlation, e.g., having similar seismic property values.When such an auto-picking mechanism is used to generate horizons, thehorizons formed at the same geological-time (t) will extend acrossfaults to generate a more accurate model. In contrast, in the firstembodiment, horizons may only be accurately formed by points (s)surrounding point (s0) that are not separated by a fault.

Although embodiments herein may describe automatically adding points inG space 104 using a seed point (x,y,z), it may be appreciated that anequivalent mechanism may be used to automatically add points in G* space106 using a seed point (u,v,t) in the flattened seismic cube grid SG*128 in G* space 106. Additional points added in G* space 106 may belocated in a neighborhood, e.g., a seismic window, of each seed pointgenerated in G* space 106.

It is contemplated that modifications and combinations of theseoperations will readily occur to those skilled in the art, whichmodifications and combinations will be within the spirit of theinvention and the scope of this invention.

Extraction of Geo-Bodies from a Seismic-Cube and a GeoChron Model

Geobodies are structures. e.g., such as a lenses, channel, levees ordune, that may have different physical properties than their surroundingregions and may introduce sedimentological discontinuities, e.g., whichare typically different from the structural discontinuities of faults.In the seismic cube grid SG* 128 in G* space 106, compared to theirsurrounding regions, geobodies are continuous geometrically, butdiscontinuous with respect to seismic property values. Geobodiesresulting from sedimentary events may be distinguished from faults whosediscontinuities in seismic property values are a result of tectonicevents.

Reference is made to FIG. 7, which illustrates visualizations of faultedhorizon H(t) 130 in G space 104 and its uvt-transformation 100 imageflattened horizon H*(t) 132 in G* space 106 for any givengeological-time (t), according to an embodiment of the invention. Thevisualization in G space 104 and its image in G* space 106 may bedisplayed on adjacent windows on a computer screen. The geological-time(t) may be altered or changed to change the corresponding faultedhorizon H(t) 130 and flattened horizon H*(t) 132 displayed. The trace ofseismic cube grid SG 126 may be displayed onto faulted horizon H(t) 130and the trace of the image of the flattened seismic cube grid SG*128 maybe displayed onto flattened horizon H*(t) 132, e.g., using a 3D texturemapping technique. This allows the seismic properties to be displayedonto faulted or folded horizon H(t) 130 and its image flattened horizonH*(t) 132 and may reveal geobodies 138, for example, representingchannels, levees or dunes or other geophysical structures. Geobody 138may be represented on a single flattened horizon H*(t) 132. Severalparts of a faulted or folded horizon H(t) 130 may be needed to visualizethe entire geobody 138.

Representations of faulted horizon H(t) 130 in G space 104 and itsuvt-transformation 100 image flattened horizon H*(t) 132 in G* space 106may be displayed to a user on a monitor, e.g., display 980 of FIG. 9.

For example, in FIG. 7, geobody 138 represents a channel, e.g.,highlighted in white. A channel is typically a continuous structureextending uninterrupted on a horizon H(t)*132 at its depositional orgeological-time (t). A dashed line 140 is drawn along geobody 138following the curve of geobody 138 on faulted horizon H(t) 130 andflattened horizon H*(t) 132. Since channels are typically continuous,geobody 138 should extend along the entire dashed line 140. However, asshown in both faulted and flattened horizons 130 and 132, geobody 138 isdiscontinuous and interrupted at regions 138′ along the dashed line 140.Accordingly, considering only the visualization of the geobodies onfaulted horizon H(t) 130 in G space 104, a user may erroneously assumethat interrupted geobody regions 138′ and 138 are two distinct geobodiesrather than one unique geobody. The visualization in the G* space 106clearly shows that the geobodies 138 and 138′ are connected parts of thesame geological structure.

According to embodiments of the invention, there is provided a systemand method for altering and correcting property models, e.g., propertymodel grid GG 120 in G space 104 and property model grid GG* 122 in G*space 106. The corrected property models 120 and 122 may then bedisplayed on corresponding present day model 108 and depositional model110, respectively, e.g., using texture mapping.

Embodiments of the invention include a new computing tool, e.g.,referred to as a “geobody-painter” or “geobody editing tool”. Thegeobody painter or editing tool may be a computing tool for extractingseismic property data associated with geobody structures. The seismicproperty data may be stored, e.g., numerically, in cells of seismic cubegrid 126 covering G space 104 and preferably in cells 124 of propertymodel grid GG* 122 covering G* space 106 (e.g., as shown in FIGS. 4 and8) where seismic property data is generally uniform (except forgeobodies 138) and therefore of a simpler form. The geobody painter mayinclude features, for example, as follows:

-   -   The geometry of the geobody painter may be selected or created        to include a pair of twin 3D volumes B* in G* space and B in G        space, e.g., referred to as a “3D brush” (which also may be        marked by the system with, e.g., a marker or cursor) which at        any time are simultaneously centered on a point (x,y,z) in G        space 104 and its uvt-transformation (u,v,t) in G* space 106.    -   The geobody painter may be moved, e.g., via user input device        965 of FIG. 9, causing dragging of the center point, onto and        across faulted horizon H(t) 130 in G space 104 and its        uvt-transformation image flattened horizon H*(t) 132 in G* space        106. When the geobody painter is moved or used in G space 104, a        simultaneous and corresponding movement or usage may be executed        in G* space 106, and vice versa.    -   The geobody painter may have “painting” and “erasing” modes in        which the seismic property data stored in cells 124 of the        property model grid GG* 122 covering G* space 106 may be edited.        Geobody-Painter Definition

Reference is made to FIG. 8, which schematically illustratesvisualizations of a geobody painter 3D marker, cursor, editing tool,e.g., including a pair of twin volumes B 142 located in G space 104 andB* 144 located in G* space 106. Twin volumes B 142 and B* 144 may bereferred to, for example, as “brushes”. The geobody painter or editortwin brushes B 142 and B* 144 may be defined, for example, such thatbrush B 142 may be the reverse uvt-transformation 112 of brush B* 144.As a consequence, when brush B* 144 crosses the uvt-transformation of afault in G* space, its reverse uvt-transformation B 142 may includedisconnected volumes on both parts of this fault in G space.

Markers, cursors, editing tools, or brushes B 142 and B* 144 may bemoveable on-screen graphical (3D) icons, which may be controlled oroperated, e.g., by a user via user input device 965 of FIG. 9. Brushes B142 and B* 144 may be displayed on adjacent windows on a computer screenwith corresponding faulted horizon H(t) 130 in G space 104 and flattenedhorizon H*(t) 132 in G* space 106, respectively. Brushes B 142 and B*144 may operate, for example, according to one of the followingmechanisms:

-   -   1. Brushes B 142 and B* 144 may have a prismatic shape (e.g., as        shown in FIG. 8, in which a cylindrical prism is used), for        example, defined as follows:        -   a. In G* space 106, brush B* 144 moving along flattened            horizon H*(t) 132 may include:            -   i. top and bottom faces located on adjacent horizons                H*(t+dt1) and H*(t−dt2), above and below flattened                horizon H*(t) 132, respectively, e.g., defined by a                closed curve drawn on these adjacent horizons; and            -   ii. vertical lateral faces, e.g., a vertically oriented                cylinder in FIG. 8.        -   b. In G space 104, brush B 142 moving along faulted horizon            H(t) 130 is the reverse uvt-transformation of a brush B* 144            defined in G* space 106. Accordingly, brush B 142 may            include:            -   i. top and bottom faces located on adjacent horizons                H(t+dt1) and H(t−dt2), above and below faulted horizon                H(t) 130, respectively, e.g., defined by a closed curve                drawn on these adjacent horizons;            -   ii. lateral faces tangential to the IPG-lines. e.g., a                cylinder oriented along an IPG line in FIG. 8.            -   iii. If brush B* 144 moves in G* space in an area, the                uvt-transformation of which is a fault in G space, then                brush B 142 may be split in G space into distinct parts                on both sides of this fault.    -   2. Brushes B 142 and B* 144 may have any suitable shape such as,        for example, but not limited to:        -   a. a sphere or half a sphere;        -   b. an ellipsoid or half an ellipsoid; and        -   c. a polyhedron.

The geometry of the geobody painter may be selected or created in Gspace 104 or G* space 106, for example, as follows:

-   -   The closed curve shape of the top and/or bottom faces of brush B        142 or brush B* 144 may include a circle, an ellipse or a        polygon, e.g., selected by the user or pre-selected as a default        shape. The size and shape of brush B 142 or brush B* 144 may be        selected by the user or pre-selected as an initial or default        size. The size and shape of brush B 142 or brush B* 144 may be        changed, e.g., using dedicated keys on a keyboard, entering a        size number or shape model, or using a mouse-wheel or clicking a        mouse. For example:        -   the shape of brush B 142 or brush B* 144 may be selected            from a plurality of predefined options, e.g., represented by            icons in various shapes of different possible closed curves.            The desired shape may be selected, e.g., by clicking (e.g.,            pressing or clicking on an input device which controls an            on-screen cursor, indicator, button or other tool) on the            desired icon with a mouse. Alternatively, the shape of brush            B 142 or brush B* 144 may be drawn by the user;        -   the initial size or diameter of brush B 142 or brush B* 144            may be pre-selected. e.g., as a function of the settings of            the virtual camera used to view the G space 104 and G* space            106 models. For example, the initial diameter of brush B 142            or brush B* 144 may be set to span a predetermined number            (e.g., n=1, 2, . . . ) of points, vertices, facets or cells            of property grid GG 120 covering the G space 104 or property            grid GG* 122 covering the G* space 106, respectively; and        -   the size or diameter of brush B 142 or brush B* 144 may be            changed, e.g., by using dedicated keys or a mouse. For            example, the diameter of the closed curve may be increased            or decreased by moving the wheel of a mouse forwards and            backwards, respectively.    -   The closed curve shape of the top and/or bottom faces of brush B        142 or brush B* 144 may be drawn on H*(t) and duplicated to        define the same shape for the top and bottom faces, may be drawn        individually on H*(t), a first time when the user selects a top        face drawing field and a second time when the user selects a        bottom face drawing field, may be drawn on horizon H*(t+dt1) for        the top face and on H*(t−dt2) for the bottom face, or may be        drawn in a designated scratch-pad area of a geopainter user        interface. The closed curve shape may be drawn free-form or by        selecting a plurality of points defining the boarder of the        curve. For example, if the close curve is a polygon, the user        may define the curve by a series of mouse or other input device        clicks on faulted horizon H(t) 130 or its image flattened        horizon H*(t) 132.    -   The heights (dt1) and (dt2) of brush B 142 or brush B* 144 above        and below faulted horizon H(t) 130 and flattened horizon H*(t)        132, respectively, may be defined, for example, as follows:        -   Initial heights (dt1) above and (dt2) below the horizon of            brush B 142 or brush B* 144 may be, for example, equal to a            vertical step on property grid GG* 122 covering the G* space            106 and/or may be set numerically by typing a size in a            dedicated editable field of a geopainter graphical user            interface. The initial heights above and below the faulted            or flattened horizons 130 and 132 are preferably equal            (e.g., dt1=dt2).        -   The heights (dt1) above and (dt2) below the horizon of brush            B 142 or brush B* 144 may be changed. For example, heights            (dt1) and (dt2) may be increased or decreased, e.g.,            interactively by moving a cursor or by pushing dedicated            keyboard keys to increase or reduce the heights or by            numerically typing a size in a dedicated editable field of a            geobody painter graphical user interface.        -   Alternatively or additionally, the heights (dt1) above and            (dt2) below the horizon of brush B 142 or brush B* 144 may            be a function of the position of the brush in the studied            domain. For example, heights (dt1) and (dt2) of brush B* 144            may vary so that the height of brush B 142 in the direction            orthogonal to the horizon H(t) remains equal to a constant            specified by the user.

Although a prismatic shaped brush may be used in some embodiments, itmay be appreciated that a curved or otherwise non-prismatic brush may beequivalently used.

It is contemplated that modifications and combinations of this mechanismwill readily occur to those skilled in the art, which modifications andcombinations will be within the spirit of the invention and the scope ofthis invention.

Geobody-Painter Positioning and Activation

In one embodiment, faulted horizon H(t) 130 and flattened horizon H*(t)132 for a user selected or initialized geological-time (t) may bedisplayed, for example on adjacent windows, or otherwise, on a computerscreen or monitor. Brush B 142 or brush B* 144 may be positioned so thattheir respective centers CB (xCB, yCB, zCB) and CB* (uCB, vCB, tCB)remain located on faulted horizon H(t) 130 and flattened horizon H*(t)132, respectively. In alternate embodiments a faulted horizon andflattened horizon may be displayed separately, on separate monitors, oron the same monitor but not at the same time. The centers CB and CB* ofbrush B 142 or brush B* 144 may be defined, for example, as follows:

-   -   Center CB* may be the forward uvt-transformation 100 of center        CB; and    -   Center CB may be the reverse uvt-transformation 112 of center        CB*.

In the particular case where brush B* 144 is cut by the image of one orseveral faults in the G* space, its reverse uvt-transform brush B 142 inthe G space may be split into several parts on both sides of thesefaults.

In one embodiment, the geobody painter editing tool may be set on/off byselecting a dedicated key (e.g., on the keyboard or mouse) or forexample by clicking a dedicated widget on the geobody painter graphicaluser interface. When the geobody painter editing tool is “active,” thecenter CB of brush B 142 and CB* of brush B* 144 may remain on faultedhorizon H(t) 130 and flattened horizon H*(t) 132, respectively, atlocations corresponding to the position of an input device, e.g., amouse. The position of brush B 142 and brush B* 144 may be synchronizedso that whenever center CB* is moved along flattened horizon H*(t) 132,center CB is moved in a corresponding manner on faulted horizon H(t)130, and vice versa. For example, when center CB* is moved to a newposition, center CB is moved to a position defined by the reverseuvt-transformation 112 of the new position of CB*. Furthermore, whenthey are moved, brush B* 144 may remain vertically oriented in G* space106, while brush B 142 may be oriented tangential to the IPG-lines in Gspace 104.

In one embodiment, various modes of the geobody painter editing tool maybe activated, in turn, for example, as follows:

-   -   The geobody painter editing tool may be set to “painter-mode.”        e.g., when the left mouse button (or any other dedicated key) is        pressed down; and    -   The geobody painter editing tool may be set to “eraser-mode,”        e.g., when the middle or right mouse button (or any other        dedicated key) is pressed down.

Other methods of user interaction may be used. For example,alternatively or additionally a user may select a field for“painter-mode” or “eraser-mode.” In other embodiments, methods otherthan “painting” and “erasing” may be used to allow a user or a processto alter the physical properties assigned to modeled particles.

Geobody-Painter Usage and Action

The geobody-painter may be used to assign seismic and or geologicalproperties values to cells of seismic cube grid SG 126 covering G space104 or cells 124 of property grid GG* 122 covering G* space 106. Forexample, seismic properties values may be assigned to cells 124 ofproperty grid GG* 122 covering G* space 106, for example, as follows:

-   -   1) Geobody 138 may be displayed to a user on a monitor (e.g., as        shown in FIG. 7), for example:        -   a. on faulted horizon H(t) 130 in G space 104 or/and its            uvt-transformation image flattened horizon H*(t) 132 in G*            space 106 for geological-time (t); or        -   b. in a volume visualization of seismic properties, e.g.,            seismic cube grid SG 126 in G space or/and seismic cube grid            SG* 128 in G* space 106, e.g., for example using 3D texture            mapping.    -   2) Each cell 124 C* of property grid GG* 122 covering G* space        106 may be initialized with default value GProp0 for a given        geological property GProp;    -   3) A constant value GProp1 may be selected and assigned to        geobody 138. For example:        -   a. the constant value GProp1 may be selected, e.g., by a            user entering the value in a dedicated field of a graphical            interface. Otherwise an automatic or default value may be            generated by a computing device;        -   b. to detect a target geobody 138, a user may scan a            plurality of faulted horizons H(t) 130 and corresponding            flattened horizon H*(t) 132 visualized in adjacent windows            of a computer screen by changing the geological-time (t)            associated therewith, until the target geobody 138 is            visible thereon. The user may scan horizons, e.g., using a            pointing device or keyboard via user input 965 of FIG. 9.            The geological-time (t) may be changed continuously or            discretely. e.g., to change the corresponding pair of            faulted and/or flattened horizons 130 and 132 displayed on            their respective screens. For example, to change the            geological-time (t) and/or corresponding faulted and/or            flattened horizons 130 and 132 displayed, a user may, for            example:            -   i. move a mouse wheel or scrolling forward (up) and/or                backward (down) to display the faulted and/or flattened                horizons 130 and 132 corresponding respectively to                higher and lower (z) and (t) coordinates (e.g., where                higher (t) coordinates correspond to a younger horizon                deposited relatively more recently than do lower (t)                coordinates);            -   ii. move a cursor or dedicated keyboard keys or enter                the geological-time (t) in a dedicated field of a                graphical user interface.            -   iii. move a tab on a geological-time-bar to scan through                different geological-times.    -   4) When a target geobody 138 is detected. e.g., by visual        inspection of the texture map overlaid on faulted and flattened        horizons 130 and 132, e.g., as shown in FIG. 7, a user may        proceed to edit properties on or in the neighborhood of the        faulted and/or flattened horizons 130 and 132. In one        embodiment, the user may assign (or “paint”) the property value        GProp1 of the target geobody 138 to the property Gprop of the        desired points of either flattened or faulted horizons 132 and        130. The corresponding property value GProp1 may be        automatically assigned to the corresponding points of the other        horizon, e.g., faulted or flattened horizons 130 and 132 using        the reverse or/and forward uvt-transforms 112 and 100,        respectively. Transforms other than uvt-transforms 112 and/or        100 may be used. The assigned property values corresponding to        geobody 138 may be stored in a subset of cells of seismic cube        grid SG 126 in G space 104 and/or cells 124 of property grid GG*        122 in G* space 106. A process may proceed, for example, as        follows:        -   a. Select the size and shape of brush B 142 and/or, the size            and shape of brush B* 144.        -   b. Set the geobody painter editing tool to an active mode.        -   c. Use a pointing device (e.g., controlled by a keyboard or            mouse) to select a point located on the target geobody 138            to be center CB of brush B 142 and/or center CB of brush B*            144 on faulted and/or flattened horizons 130 and 132,            respectively.        -   d. To assign properties, a “painting” mode may be activated            (e.g., holding down a dedicated key such as a left button of            a mouse or the cntrl and v keys on a keyboard) and the input            device may be used to move brush B 142 or brush B* 144 along            faulted or flattened horizons 130 and 132, respectively, so            that brush B 142 or brush B* 144 traces a desired geobody            138. For example, brush B 142 and/or brush B* 144 may be            moved along dashed line 140 outlining the regions where a            geobody is to be added. When in painting mode, brush B 142            or brush B* 144 may assign the same property value. e.g.,            GProp1, for the property GProp, to all regions traced by the            brush, e.g., all points located within the closed curve of            the intersection of brush B 142 or brush B* 144 with faulted            and/or flattened horizons 130 or 132, respectively. The            property value GProp1 may be stored in cells of seismic cube            grid SG 126 in G space 104 and/or in cells 124 of property            grid GG* 122 in G* space 106, e.g., for all cells with            centers corresponding to the traced points of faulted or            flattened horizons 130 and 132, respectively.        -   e. To delete properties or erase a region painted in            step (d) above, an “erase” mode may be activated (e.g.,            holding down a dedicated key such as a right button of a            mouse or the cntrl and x keys on a keyboard) and the input            device may be used to move brush B 142 or brush B* 144 along            faulted or flattened horizons 130 and 132, respectively, so            that brush B 142 or brush B* 144 traces the region of            geobody 138 to be removed. When in erase mode, brush B 142            or brush B* 144 may assign the initial or default property            value. e.g., GProp0, for the property GProp, to all regions            traced by the brush. The property value GProp0 may be stored            in cells seismic cube grid SG 126 in G space 104 and/or in            cells 124 of property grid GG* 122 in G* space 106. e.g.,            for all cells with centers corresponding to the traced            points of faulted or flattened horizons 130 and 132,            respectively.        -   f. Optionally, the shape, size, and height of brush B 142            and/or brush B* 144 may be changed.    -   5) STOP

Other operations or series of operations may be used. Although thedescription above describes changing property value by tracing a regionwith brush B 142 and/or brush B* 144, embodiments of the invention mayinclude manipulation the shape or size of geobodies 138 in any manner.e.g., including extending, shifting, translating, rotating, shrinking,elongating, or otherwise altering the property values of faulted and/orflattened horizons 130 and 132. In each of these embodiments, an inputdevice may be used to change the set of points or cells to which thegeobodies 138 property values are assigned.

In one embodiment, when geobody 138 is partially formed and already hasproperty values assigned thereto, to further edit geobody 138 (e.g., toelongate geobody 138), the property values already assigned to geobody138 may be copied or sampled (e.g., by clicking on a point of geobody138 when in a “sample” or “copy” editing mode) and then pasted ondesired regions where the geobody 138 may be added (e.g., by clicking ona point of geobody 138 when in a “paste” or “painting” editing mode).

It may be appreciated that painting or assigning property values tovertices, cells or facets changes the data associated with modeledpoints. For example, when a coordinate (x,y,z) or its uvt-transformation(u,v,t) is painted with a property p0, the coordinate is transformed to(x,y,z,p0) or (u,v,t,p0), respectively. Thus, the geological data of ageophysical subsurface structure, e.g., a particle of sediment,represented by the painted coordinates is altered. In contrast, othermechanisms change the visual aspects of pre-existing properties, forexample, by coloring, painting or altering the opacity of dataassociated with the pre-existing properties, but do not change theproperties themselves in the seismic cube grid SG* 128. For example,other mechanisms may change the color for property p0 from red topurple, or from transparent to opaque, but these mechanisms do not add aproperty value p0 to (x,y,z) or (u,v,t) or do not change a propertyvalue from p0 to p1 at these points. For example, a user selects a timerange and the horizons corresponding to structures deposited in thattime range are made opaque, while horizons corresponding to structuresdeposited at outside that time range are made transparent. The timerange may be altered to make changes in the horizons that are opaque andtransparent. In this and other conventional modeling mechanisms, theuser merely alters the visual representation of static data and does notalter the actual data itself. While these mechanisms are imperfect,embodiments of the invention may be used in combination therewith.

Other conventional mechanisms teach painting geobodies directly on aseismic cube grid SG 126 in G space 104 without using property grid GG*122 in G* space 106 or uvt-transformations 100 or 112. Embodiments ofthe invention provide significant differences and advantages over suchmechanisms, for example, by painting properties on a property grid GG*122 in G* space 106. Some advantages of embodiments of the invention maybe seen, in particular, in regions where geobodies are cut by faults,for example as follows (not all advantages may be seen in allembodiments of the invention):

-   -   Conventional mechanisms paint geobodies in G space 104, where        property values are discontinuous across faults 109. When        conventional mechanisms extract and paint geobodies directly on        seismic cube grid SG 126 in G space 104, the painting is stopped        as soon as a fault is reached. Accordingly, conventional geobody        painters cannot paint a geobody that extends to opposite sides        of a fault.    -   In contrast, embodiments of the invention may paint and extract        geobodies 138 in G* space 106, where faults 109 vanish.        Accordingly, in G* space 106, geobodies 138 may be extracted and        painted without interruption from faults or discontinuities. In        some embodiments, geobodies 138 may extract and paint points        continuously and without interruption in G* space 106, where the        points in G* space 106 correspond to points on opposite sides of        a fault 109 in G space 104. Once geobodies 138 are painted in G*        space 106, the new property values are applied to points on        opposite sides of the fault 109 in G space 104, e.g., using the        reverse uvt transformation 112. Accordingly, embodiments of the        invention may paint and extract geobodies 138 continuously        across faults 109.

In some embodiments, the geobody painter editing tool may be used todraw an isolated geobody 138 on property grid GG* 122 in G* space 106,e.g., not overlaid over a pre-existing model or seismic cube. Geobody138 may be drawn. e.g., in 3D, on a scratch-pad or using an editingapplication. For example, an isolated geobody 138 may be useful forgenerating 3D training images in connection with multipointgeo-statistics models. For example, a process may proceed as follows:

-   -   1) Faulted or flattened horizons 130 or 132 at a specific        geological-time (t) may be selected, e.g., by a user via user        input 965 of FIG. 9, for drawing a geobody 138.    -   2) Each cell C* 124 of property grid GG* 122 covering G* space        106 may be initialized with a default value GProp0 for a        geological property GProp.    -   3) A constant value GProp1 may be selected and assigned to        geobody 138. For example:        -   a. the constant value GProp1 may be selected, e.g., by            entering the value in a dedicated field of a graphical            interface. Otherwise an automatic or default value may be            generated by a computing device;        -   b. A user may scan one or more faulted horizons H(t) 130 in            G space 104 and corresponding flattened horizon H*(t) 132 in            G* space 106, e.g., visualized in adjacent windows of a            computer screen by for example changing the            geological-time (t) associated therewith. For example, to            change the geological-time (t) and/or corresponding faulted            and/or flattened horizons 130 and 132 displayed, a user may,            for example:            -   i. move a mouse wheel or scrolling forward (up) and/or                backward (down) to display the faulted and/or flattened                horizons 130 and 132 corresponding respectively to                higher and lower (z) and (t) coordinates (e.g., where                higher (t) coordinates correspond to a younger horizon                deposited relatively more recently than do lower (t)                coordinates);            -   ii. move a cursor or dedicated keyboard keys or enter                the geological-time (t) in a dedicated field of a                graphical user interface.            -   iii. move a tab on a geological-time-bar to scan through                different geological-times.    -   4) When a user selects a desired faulted and/or flattened        horizons 130 and 132 to paint a geobody, the user may assign (or        “paint”) the property value GProp1 associated with the geobody        138 to the property Gprop of the desired points of either        flattened or faulted horizons 132 and 130. The assigned property        values corresponding to geobody 138 may be stored in a subset of        cells 116 of property grid GG 120 in G space 104 and preferably        in cells 124 of property grid GG* 122 in G* space 106. A process        may proceed, for example, as follows:        -   a. The size and shape of brush B 142 and/or brush B* 144 may            be selected, e.g., by a user via user input 965 of FIG. 9.        -   b. The geobody painter editing tool may be set to an active            mode, e.g., by a user selecting as dedicated key of user            input 965 of FIG. 9 such as a left button on a mouse.        -   c. Use a cursor or editing device (e.g., controlled by a            keyboard or mouse) to select a point to be drawn as center            CB of brush B 142 and/or center CB of brush B* 144 on            faulted and/or flattened horizons 130 and 132, respectively.        -   d. To assign properties, a “painting” mode may be activated            (e.g., holding down a dedicated key such as a left button of            a mouse or the cntrl and v keys on a keyboard) and the input            device may be used to move brush B 142 or brush B* 144 along            faulted or flattened horizons 130 and 132, respectively, so            that brush B 142 or brush B* 144 traces the desired geobody            138. For example, brush B 142 and/or brush B* 144 may be            moved to outline any regions where the geobody is desired.            When in painting mode, brush B 142 or brush B* 144 may            assign the same property value. e.g., GProp1, for the            property GProp, to all regions traced by the brush, e.g.,            all points located interior to brush B 142 or brush B* 144.            For each cell of a of property grid with a center            corresponding to a traced point, the property value GProp1            may be stored in the cell. Storing a property value in a            cell may mean that the property value may be stored in a            memory or storage in a way so that it is associated with,            within, or linked to stored cell data. For example, property            value may be stored in cells seismic cube grid SG 126 in G            space 104 and preferably in cells 124 of property grid GG*            122 in G* space 106.        -   e. To delete properties or erase a region painted in            step (d) above, an “erase” mode may be activated (e.g.,            holding down a dedicated key such as a right button of a            mouse or the cntrl and x keys on a keyboard) and the input            device may be used to move brush B 142 or brush B* 144 along            faulted or flattened horizons 130 and 132, respectively, so            that brush B 142 or brush B* 144 traces a desired region of            geobody 138 to be deleted. When in erase mode, brush B 142            or brush B* 144 may assign the initial or default property            value. e.g., GProp0, for the property GProp, to all regions            traced by the brush. The property value GProp0 may be stored            in cells 116 of grid GG 120 and/or cells of seismic cube            grid SG 126 in G space 104 and/or in cells 124 of property            grid GG* 122 in G* space 106, e.g., for all cells with            centers corresponding to the traced points of faulted or            flattened horizons 130 and 132, respectively.        -   f. Optionally, the shape, size, and height of an editing            tool such as brush B 142 and/or brush B* 144 may be changed            (or edited).    -   5) STOP

Other operations or series of operations may be used, and other specificuser interaction systems may be used.

Painting the Seismic Cube

Once property values for a property GProp are stored in cells 124 ofproperty grid GG* 122 in G* space 106, the same property values may betransferred to cells of the seismic cube grid SG 126 in G space 104(e.g., or vice versa). For example, a process may proceed as follows:

-   -   1. for each cell C of the seismic cube grid SG 126:        -   a. A reference point RC may be determined. The reference            point RC may be inside the cell, for example, the center            point of the cell.        -   b. A corresponding reference point RC* in G* space 106 may            be generated that is the uvt-transformation 100 of the            reference point RC.        -   c. Cell C* 124 of property grid GG* 122 in G* space 106 may            be identified to contain the reference point RC*.        -   d. The property value GProp stored in cell C* 124 of            property grid GG* 122 in G* space 106 may be copied in cell            C of seismic cube grid SG 126 in G space 104. Storing a            property value in cell C or 124 may mean that the property            value is stored in a memory or storage (e.g., memory 950 of            FIG. 9) in a way so that it is associated with, within, or            linked to the cell or cell data.    -   2. STOP

According to these operations, when a property value GProp is assignedto a first point RC* or corresponding cell 124 in a first propertymodel, e.g., grid GG* 122 or flattened seismic cube 128, the sameproperty value GProp is assigned to a second point RC or correspondingcell 116 in a second property model. e.g., seismic grid GG 120 orfaulted seismic cube 126, wherein the second point RC is the image ofthe first point RC*, e.g., as defined by the reverse uvt-transformation112 or another local transform, between the first seismic property modeland the second seismic property model.

Other operations or series of operations may be used.

Reference is made to FIG. 9, which schematically illustrates a systemincluding a transmitter, receiver and computing system in accordancewith an embodiment of the present invention. Methods disclosed hereinmay be performed using a system 905 of FIG. 9. In other embodiments,methods used herein may be performed by different systems, havingdifferent components.

System 905 may include a transmitter 990, a receiver 920, a computingsystem 930, and one or more display(s) 980. The aforementioned data,e.g., seismic data used to form intermediate data and finally to modelsubsurface regions, may be created by processing data generated bytransmitter 990 and received by receiver 920. Intermediate data may bestored in memory 950 or other storage units. The aforementionedprocesses described herein may be performed by code, instructions orsoftware 960 being executed by processor 940 manipulating the data.

Transmitter 990 may transmit signals, for example, acoustic waves,compression waves or other energy rays or waves, that may travel throughsubsurface (e.g., below land or sea level) structures. The transmittedsignals may become incident signals that are incident to subsurfacestructures. The incident signals may reflect at various transition zonesor geological discontinuities throughout the subsurface structures. Thereflected signals may include seismic data.

Receiver 920 may accept reflected signal(s) that correspond or relate toincident signals, sent by transmitter 990. Transmitter 990 may transmitoutput signals. The output of the seismic signals by transmitter 990 maybe controlled by a computing system, e.g., computing system 930 oranother computing system separate from or internal to transmitter 990.An instruction or command in a computing system may cause transmitter990 to transmit output signals. The instruction may include directionsfor signal properties of the transmitted output signals (e.g., such aswavelength and intensity). The instruction to control the output of theseismic signals may be programmed in an external device or program, forexample, a computing system, or into transmitter 990 itself.

Computing system 930 may include, for example, any suitable processingsystem, computing system, computing device, processing device, computer,processor, or the like, and may be implemented using any suitablecombination of hardware and/or software. Computing system 930 mayinclude for example one or more processor(s) 940, memory 950 and code,instructions or software 960. Data 955 generated by reflected signals,received by receiver 920, may be transferred, for example, to computingsystem 930. The data may be stored in the receiver 920 as for exampledigital information and transferred to computing system 930 byuploading, copying or transmitting the digital information. Processor940 may communicate with computing system 930 via wired or wirelesscommand and execution signals.

Memory 950 may include cache memory, long term memory such as a harddrive, and/or external memory, for example, including random accessmemory (RAM), read only memory (ROM), dynamic RAM (DRAM), synchronousDRAM (SD-RAM), flash memory, volatile memory, non-volatile memory, cachememory, buffer, short term memory unit, long term memory unit, or othersuitable memory units or storage units. Memory 950 may storeinstructions (e.g., software 960) and data 955 to execute embodiments ofthe aforementioned methods, steps and functionality (e.g., in long termmemory, such as a hard drive).

Data 955 may include, for example, raw seismic data collected byreceiver 920, instructions for building a mesh, instructions forpartitioning a mesh, instructions for generating a seismic cube, seismicgrid, seismic property model and instructions for processing thecollected data to generate a model, or other instructions or data.Memory 950 may store a geological-time function, a model representing astructure when it was originally deposited (e.g., in uvt-space) and/or amodel representing the corresponding structure in a present day orrecent time period (e.g., in xyz-space). Memory 950 may store seismicproperty models, e.g., a seismic property grid and seismic cube, in Gspace and/or G* space and a mesh for generating each seismic propertymodel. Geological models in G space and/or G* space may be, for example,a digital rendering of seismic data, e.g., defined by cells, nodes,vertices, facets, voxels, pixels, etc., that estimate or approximate thelikely position of groups of underground particles. Memory 950 may storethe cells, nodes, voxels, etc., associated with the models and the modelgrids. Memory 950 may also store instructions and data allowing aprocessor to execute global transformation functions (e.g., forwardand/or reverse uvt-transformations 100 and 112 of FIG. 1) to transformpoints in the present day model in G space to the past depositionalmodel in G* space, and vice versa. Memory 950 may also storeinstructions and data allowing a processor to execute localtransformation functions, e.g., local forward and/or reverseuvt-transformations, to transform a designated subset of points in thepresent day model in G space to corresponding subset of points in thepast depositional model in G* space, and vice versa. Data 955 may alsoinclude intermediate data generated by these processes and data to bevisualized, such as data representing graphical models to be displayedto a user. Memory 950 may store intermediate data. System 930 mayinclude cache memory which may include data duplicating original valuesstored elsewhere or computed earlier, where the original data may berelatively more expensive to fetch (e.g., due to longer access time) orto compute, compared to the cost of reading the cache memory. Cachememory may include pages, memory lines, or other suitable structures.Additional or other suitable memory may be used.

Computing system 930 may include a computing module havingmachine-executable instructions. The instructions may include, forexample, a data processing mechanism (including, for example,embodiments of methods described herein) and a modeling mechanism. Theseinstructions may be used to cause processor 940 using associatedsoftware 960 modules programmed with the instructions to perform theoperations described. Alternatively, the operations may be performed byspecific hardware that may contain hardwired logic for performing theoperations, or by any combination of programmed computer components andcustom hardware components.

Embodiments of the invention may include an article such as a computeror processor readable medium, or a computer or processor storage mediumsuch as for example a memory, a disk drive, or a USB flash memory,encoding, including or storing instructions. e.g., computer-executableinstructions, which when executed by a processor or controller, carryout methods disclosed herein.

Processor 930 may perform various methods described herein. For example,processor 940 may generate a geological time function t(x,y,z) andpaleo-geographic coordinate functions u(x,y,z) and v(x,y,z), accordingembodiments of the invention. The geological time function t(x,y,z) maybe an arbitrary monotonic increasing function of time. For example, thegeological time function t(x,y,z) may provide the relative times or timeorder when structures were deposited, not necessarily the real times.

Processor 940 may generate a 3D uvt-transformation based on the one ormore global functions or rules, which when applied to each point (x,y,z)generate geological time function t(x,y,z) and paleo-geographiccoordinate functions u(x,y,x) and v(x,y,z). The uvt-transformation maytransform data points in models between G space and G* space. Whenprocessor 940 receives an indication to locally change theuvt-transformation for a subset of points in the models (e.g., via inputdevice 965), processor 940 may generate an updated and locally changedversion of the uvt-transformation to replace the uvt-transformation forthe subset of points. The updated or new uvt-transformation transformsthe subset of points differently than the initial uvt-transformation atleast for the local subset of points. The initial and newuvt-transformations may include parameterizations between G space and G*space to transform a present day model in G space of a discontinuousfaulted horizon to a single substantially continuous horizon in G*space.

Display 980 may display data from transmitter 990, receiver 920, orcomputing system 930 or any other suitable systems, devices, orprograms, for example, an imaging program or a transmitter or receivertracking device. Display 980 may include one or more inputs or outputsfor displaying data from multiple data sources or to multiple displays.For example display 980 may display visualizations of subsurface modelsincluding subsurface features, such as faults, horizons andunconformities.

Display may 980 may display a faulted horizon H(t₀) in G space and aflattened horizon H*(t₀) in G* space. For example, the models may bedisplayed separately, adjacent to, or overlapping each other. In oneembodiment, a user may scan through a plurality of faulted horizons H(t)and/or corresponding flattened horizon H*(t) visualized in adjacentwindows on display 980 by changing the geological-time (t) associatedtherewith. The geological-time (t) and/or corresponding faulted and/orflattened horizons displayed may be changed, for example, by moving amouse wheel or scrolling forward (up) and/or backward (down) to displaythe faulted and/or flattened horizons corresponding to higher and lower(z) or (t) coordinates, respectively. Higher (t) coordinates typicallycorrespond to a younger horizons deposited relatively more recently thanlower (t) coordinates. In another embodiment, geological-time (t) and/orcorresponding faulted and/or flattened horizons displayed, may bechanged, for example, by moving a cursor or dedicated keyboard keys orby entering a desired geological-time (t) in a dedicated field of agraphical user interface. In yet another embodiment, the geological-time(t) and/or corresponding faulted and/or flattened horizons displayed,may be changed, for example, by moving a tab on a geological-time-bar toscan through different geological-times.

When a faulted horizon H(t₀) in G space and/or a flattened horizonH*(t₀) in G* space are displayed on display 980, a user may, forexample, inspect the horizons to determine any problematic points orpoints to be changed. For example, the uvt-transformation mayerroneously transform a point in G space to the wrong flattened horizonH*(t) in G* space using the uvt-transformation. Since property valuesare ideally exactly or approximately constant across horizons in G spaceand horizontal cross sections in G* space, such an erroneous point maybe detected easily, for example, by a user inspecting a display of theflattened horizon H*(t) in G* space. The user may quickly identify anystray points significantly deviating from the ideally constant propertyvalues across the otherwise flattened horizons or horizontal crosssections. For example, when a color map is used, e.g., red correspondingto one property value Gprop1 and purple to another property valueGprop2, a stray point may appear for example as a purple dot in anotherwise red horizontal section (other color schemes or graphicaltechniques may be used). The user may click the purple point in a‘delete’ mode, activate an ‘add’ mode, and select another red point toreplace the purple point, e.g., located in the neighborhood of thepurple point. The user may identify points to be changed and the ‘add’or ‘delete’ modes via input device 965, e.g., controlled to click on orhighlight the points on display 980.

Alternatively, processor 940 may automatically identify any problematicpoints or points to be changed by measuring the standard deviation ofproperty values across a horizons or horizontal cross sections in G*space. When processor 940 measures standard deviation values for aproperty that is greater than a predetermined threshold in a localregion (e.g., a neighborhood of a point), processor 940 mayautomatically identify the deviating point or points and may select thepoint to be changed and corrected.

When points in the models are locally changed or edited, e.g., added,deleted, moved, or otherwise rearranged, the uvt-transformation (e.g.,including the direct and reverse uvt-transformations) associated withthe initial locations of the points may be changed. Thus, editing thelocations of points, cells, facets, voxels or other features in one orboth of the models in G and/or G* space, involves editing theuvt-transformation itself.

When processor 940 accepts an indication (e.g., from a user) to changethe uvt-transformation for the subset of points in the models (e.g.,selected automatically by processor 940 or by a user via input device965), processor 940 may generate a new uvt-transformation replacing theinitial uvt-transformation. To change the location of each point in themodels, e.g., by adding, moving, or rearranging, the point may have acorresponding point in the other model and a new map between thosecorresponding points may be defined by re-computing theuvt-transformation. The new uvt-transformation may take into accountdeleted sampling points, new sampling points, or change old samplingpoints whose location has changed. When the locations of points in onemodel are altered, the other model may be automatically updatedaccordingly to the new uvt-transformation. Processor 940 may, forexample, in response to a user changing the location of points in one ofthe models, automatically generate a new uvt-transformation to render acorresponding change in location for corresponding points in the otherone of the models.

In one embodiment, a system and method is provided for editing models ofphysical geological structures. Corresponding points may be edited inthe present day and past depositional models and a newuvt-transformation may be generated, where the new uvt-transformationdefines the correspondence between the points edited in the present daymodel and the points edited to the past depositional model.Corresponding points may be added, moved or deleted from the present dayand past depositional models and the new uvt-transformation may takethose changes into account. The direct uvt-transformation may beinjective (i.e., each point in G space has an image in G* space, but notall points in G* space. e.g., eroded points, have an image in G* space).In some embodiments, moving a point from a first location to a secondlocation may be equivalent to deleting the point at the first locationand adding a new point at the second location.

Display 980 may display the models in separate pages or windows (oralternately on the same page or window) and a user may select one of themodels (e.g., by clicking a ‘G space’ or ‘G* space’ button with apointing device such as a mouse or by scrolling between the models). Auser may select a display option to temporarily hide or reveal features,e.g., seismic property models. Property models may be displayed as forexample color, texture and/or symbol maps. Property models may bedisplayed separately, overlaying or instead of other geometric models.Processor 940 may overlay property models onto flattened or faultedhorizons or flattened or faulted seismic cubes, e.g., using 3D texturemapping mechanisms.

In one embodiment, the user may edit a property model in the present dayor depositional models and the same edit may be automatically renderedon the other model, by processor 940 executing a uvt-transformation. Inthis way, a user may simultaneously view the property changes tostructures in the present and depositional times. Processor 940 mayaccept graphical user input, e.g., from a property editing toolcontrollable by input device 965, for editing property values assignedto points in a model in G space or G* space. The editing tool may allowa user to operate in modes such as “painting” and “erasing” modes. Inthe “painting” mode, the editing tool may be used to assign propertyvalues to points in G space or G* space (e.g., using brushes 142 or 144of FIG. 8, respectively), using the brush to trace the points. Theproperty values assigned may be designated. e.g., to represent aparticular geobody such as a channel or dune. In the “erase” mode, theediting tool may be used to delete a property value in G space or G*,e.g., resetting or re-assigning the property values of all the pointstraced by the brush, to their initial values before brushing occurred.Multiple different properties may be changed accordingly. For example,to paint three distinct geobodies on a horizon in G space or G* space,three separate property values may be used.

To begin painting, a user may select a faulted horizon H(t₀) in G spaceand a flattened horizon H*(t₀) in G* space to be displayed on displaymay 980. For example, the models may be displayed separately, adjacentto, or overlapping each other. In one embodiment, a user may scanthrough a plurality of faulted horizons H(t) and/or correspondingflattened horizon H*(t) visualized in adjacent windows on display 980.Processor 940 may provide a graphical user interface for a user tocontrol and edit property values on faulted horizon H(t₀) in G space anda flattened horizon H*(t₀) in G* space. The graphical user interface mayprovide options for a user to select or create the size, height andshape of the brush or property editing tool. The graphical userinterface may include a plurality of modes. e.g., active (for editing),inactive (for viewing), paint mode, erase mode, extract geobody mode,copy geobody mode, etc. Processor 940 may receive activation of paintmode and movement commands. e.g., from input device 965, for moving theediting brush. When in painting mode, the editing brush may assign thesame user defined property value, e.g., GProp1, to all regions traced bythe brush, e.g., all points on the horizons located within the brush.When in erase mode, the initial or default property value, e.g., GProp0,may be assigned to all regions traced by the brush. The property valuesmay be stored in cells of seismic cube grid SG and/or property grid GGin G space and/or in cells of seismic cube grid SG* or property grid GG*in G* space, e.g., for all cells traced by the brush.

When property values assigned to points in a first model are initiallychanged, processor 940 may automatically alter the second modelaccordingly. For example, processor 940 may assign the same editedproperty values to corresponding points of the second model, wherein thecorresponding points in the second model are the image of the initiallychanged points in the first model. In one embodiment, once propertyvalues for a property are stored in cells in G space or G* space, thesame property values may be transferred to corresponding cells in theother space, e.g., G* space or G space, respectively. Property valuesmay preferably be changed initially in the past depositional model in G*space and then automatically edited in the present day model in G space.In one embodiment, when the property values associated with a geobodyare first edited at points of the past depositional model correspondingto points on opposite sides of a fault in the present day model, theproperty values associated with a geobody may be automatically edited toextend across opposite sides of the fault in the present day model.

Input device(s) 965 may include one or more of, for example, a keyboard,pointing device (e.g., mouse, trackball, pen, touch screen), or cursordirection keys, communicating information and command selections toprocessor 940. Input device 965 may communicate user directioninformation and command selections to the processor 940. For example, auser may use input device 965 to edit the locations or property valuesof points in the models (e.g., by pointing a ‘select’, ‘add’, ‘delete’,‘paint’, ‘erase’ button on a display 980 monitor adjacent to the modelusing a cursor controlled by a mouse).

Processor 940 may include, for example, one or more processors,controllers, central processing units (“CPUs”), or graphical processingunits (“GPUs”). Software 960 may be stored, for example, in memory 950.Software 960 may include any suitable software, for example, DSIsoftware.

Processor 940 may generate corresponding models in G space and G* space,for example, using data 955 from memory 950. In one embodiment, a modelmay simulate structural, spatial, seismic or geological properties of asubsurface region, such as, porosity or permeability throughoutgeological terrains.

Processor 940 may initially generate a three dimensional mesh, lattice,or collection of nodes that spans or covers a domain of interest. Thedomain may cover a portion or entirety of the three-dimensional spacesought to be modeled. Processor 940 may automatically compute the domainto be modeled and the corresponding mesh based on the collected seismicdata so that the mesh covers a portion or the entirety of thethree-dimensional space from which seismic data is collected (e.g., thestudied subsurface region). Alternatively or additionally, the domain ormesh may be selected or modified by a user, for example, enteringcoordinates or highlighting regions of a simulated optional domain ormesh. For example, the user may select a domain or mesh to model aregion of the Earth that is greater than a user-selected subsurfacedistance (e.g., 100 meters) below the Earth's surface, a domain thatoccurs relative to geological features (e.g., to one side of a knownfault or riverbed), or a domain that occurs relative to modeledstructures (e.g., between modeled horizons H(t₁) and H(t₁₀₀)). Processor940 may execute software 960 to partition the mesh or domain into aplurality of three-dimensional (3D) cells, columns, or other modeleddata (e.g., represented by voxels, pixels, data points, bits and bytes,computer code or functions stored in memory 950). The cells or voxelsmay have hexahedral, tetrahedral or any other polygonal shapes, andpreferably three-dimensional shapes. Alternatively, data may includezero-dimensional nodes, one-dimensional segments, two-dimensional facetand three-dimensional elements of volume, staggered in athree-dimensional space to form three-dimensional data structures, suchas cells, columns or voxels. The cells may preferably conform to andapproximate the orientation of faults and unconformities. Each cell mayinclude faces, edges and/or vertices. Each cell or node may correspondto or represent one or more particles of a subsurface material in theEarth (e.g., a cell may include many cubic meters of particles). Eachcell, face, edge, vertex or node may be located. e.g., in a grid orlattice, throughout the model. In contrast, a point of the model may belocated at any location in the modeled domain, for example, in a cellbetween adjacent nodes.

As shown in FIG. 4, model 110 in G* space 106, i.e., modeling propertiesat depositional geological time (the time the structures being modeledwere originally deposited) may be generated using a regular mesh, suchas property grid 122 (e.g., having a uniform lattice or grid structureor nodes and cells 124). In contrast, model 108 of FIG. 1 may begenerated using an irregular mesh (having an irregular lattice orarrangement or nodes or cells 116). Again in reference to FIG. 9, datacollected by receiver 920 after the time of deposition in a present dayor present time period, faults and unconformities that have developedsince the original time of deposition, e.g., based on tectonic motion,erosion, or other environmental factors, may disrupt the regularstructure of the geological domain. Accordingly, an irregular mesh maybe used to model present day geological structures, for example, so thatat least some faces, edges, or surfaces of cells may be orientedparallel to faults or unconformities, and may not be intersectedthereby. In one embodiment, a mesh may be generated based on datacollected by receiver 920, alternatively, a generic mesh may begenerated to span the domain and the data collected by receiver 920 maybe used to modify the structure thereof. For example, the data collectedmay be used to generate a set of point values at “sampling point.” Thevalues at these points may reorient the nodes or cells of the mesh togenerate a model that spatially or otherwise represents the geologicaldata collected from the Earth. Other or different structures, datapoints, or sequences of steps may be used to process collectedgeological data to generate a model. The various processes describedherein (e.g., generating models) may be performed by manipulating suchmodeling data.

The geological-time function t(x,y,z) and the paleo-geographiccoordinates u(x,y,z) and v(x,y,z) may generate a uvt-transformationdefined at a finite number of nodes or sampling points based on realdata corresponding to a subsurface structure, e.g., one or moreparticles or a volume of particles of Earth. These functions may beapproximated between nodes of a mesh (e.g., grid GG 120 in G space 104in FIG. 1) to continuously represent the subsurface structure, oralternatively, depending on the resolution in which the data is modeledmay represent discrete or periodic subsurface structures, e.g.,particles or volumes of Earth that are spaced from each other. A localtransformation may be considered in one embodiment discreteparameterizations of a finite number of points with locations differentthan that defined by the global transformation.

It may be appreciated that representing seismic structures, features andlocations in either the present day model or past depositional model mayrefer to creating an estimate or approximation of these locations andfeatures in their respective models. Although ideally these estimates orapproximations of locations and features are accurate, in some cases,for example, the may be only partially accurate or inaccurate.

In one embodiment, input data to computing system 930 may includehorizon sampling points, including well paths, well markers, or otherdata. Representations of sampling points may be displayed on the horizonmodel. Some sampling points, e.g., corresponding to erroneous points inG* space forming non-uniform seismic property values, may be removed ormoved in the model or may have their property values changed.

Fault surfaces, horizon surfaces, model boundaries (e.g., as lines ortransparent surfaces) may be modeled and displayed on display 980. Thepaleo-geographic coordinate functions u(x,y,z) and v(x,y,z) of theuvt-transformation may be “painted” on horizons as a grid (e.g., eachline of the grid may correspond to a constant value for function (u) orthe function (v)). The model may be displayed, for example in geologicalspace or in geo-chronological space or both at the same time.

Reference is made to FIG. 10, which is a flowchart of a method formodeling a subsurface structure at a time period when the structure wasoriginally formed, which may be performed using system 905 of FIG. 9.Other operations or series of operations may be used, and the exact setof operations shown below may be varied.

In operation 1000, a computing device (e.g. processor 940 of FIG. 9) mayaccept seismic data (e.g., associated with seismic cubes) and/orgeologic data (e.g., well markers along well paths). The seismic datamay include raw data, e.g., signals received from the Earth, such as,acoustic waves, compression waves or other energy rays or waves, thatmay travel through subsurface (e.g., below land or sea level)structures. Alternatively, the computing device may accept dataprocessed from the raw data or other data not directly collected fromthe Earth, but that is simulated to represent data within the Earth. Forexample, a present day model may represent actual structures within theEarth, while a depositional model is a simulation of how thosestructures appeared in the past when they were deposited. Furthermore,seismic and geological data may be edited, added, drawn, created, ormanipulated, e.g., within a model.

In operation 1010, the computing device may generate a present day modelhaving points representing present locations of the physical geologicalstructures.

In operation 1020, to generate a second past depositional model, thecomputing device may generate a 3D transformation (e.g.,uvt-transformation 100 and 112 of FIG. 1) from the present day model tothe past depositional model having points representing locations wherethe physical geological structures were originally deposited. Thetransformation may be based on one or more global functions initiallyapplied to all points in the models.

In operation 1030, the computing device may accept, e.g. from a user, anindication to locally change the transformation for a subset of pointsin the models. The subset of points may be accepted from a userselecting the subset of points from one of the models, e.g., via userinput device(s) 965. To identify points to change, in one embodiment, auser may inspect seismic property values displayed on a pastdepositional model. Since seismic properties are ideally horizontallyuniform throughout the model, any variations or stray points deviatingfrom the ideal uniform behavior may be easily identified and selected bythe user. Alternatively, the subset of points may be selectedautomatically by a computing device. In one embodiment, the subset ofpoints may include points having seismic property values that aresubstantially different than the seismic property values of other pointslocated on the same horizon or horizontal cross-section of the pastdepositional model. The uvt-transformation as it applies to the subsetof points may be inaccurate and may be edited and corrected.

In operation 1040, the computing device may locally change thetransformation to fit the changes for the subset of points indicated instep 1030. For each point changed in the models, e.g., added, moved, orrearranged, the point may have a corresponding changed or pre-existingpoint in the other model and the map between those points may be definedby the locally changed or altered version of the uvt-transformation. Thelocally change (new) uvt-transformation may differ from the initialuvt-transformation in that the new uvt-transformation is typically notgenerated based on the same data (set of sampling points) as the initialuvt-transformation. The new uvt-transformation may be re-interpolated tofit translated, rotated or otherwise moved sampling points, new or addedsampling points, deleted or removed sampling points, e.g., to replacethe deleted subset of points, or change the correlation between points.When points in one model are altered, the other model may beautomatically updated accordingly by uvt-transformation for each alteredpoint. The computing device may, for example, in response to a userselecting a subset of points to be changed in one of the models, mayautomatically generate the uvt-transformation between the subset ofpoints and a second subset of points in the other model.

In operation 1050, a display device (e.g. display 980 of FIG. 9) maydisplay an altered or updated version of the present day anddepositional models where the points in the models are related by thelocally changed uvt-transformation.

In operation 1060, if remaining errors are detected in either thepresent day or past depositional model, a process may return to step1030 to iteratively generate one or more additional altered models, forexample, incrementally improving in accuracy in each iteration.

The computing device may accept the data used in the aforementionedoperations as for example a set of data reflected from a subsurfacegeological feature, or such data augmented by another process.

Reference is made to FIG. 11, which is a flowchart of a method fortransforming subsurface models modeling a terrain, which may beperformed using system 905 of FIG. 9. Other operations or series ofoperations may be used, and the exact set of steps shown below may bevaried.

In operation 1100, a computing device (e.g. processor 940 of FIG. 9) mayaccept seismic (e.g., a seismic cube) and/or geologic data (e.g., wellmarkers along well paths).

In operation 1110, the computing device may generate a first model and asecond model, wherein one model represents present locations of thephysical geological structures and the other model represents locationswhere the physical geological structures were originally deposited inthe past. The first and second models are related by a transformation,e.g., a 3D forward and reverse uvt transformation. Other transformationsor underground modeling systems may be used.

In operation 1120, the computing device may display the first model andthe second model on a display (e.g. display 980 of FIG. 9). The firstand second models may be displayed in adjacent, sequential, alternate,and/or separate windows of a monitor.

In operation 1130, the computing device may accept. e.g., from a useroperating an input device, a graphical user input for editing geologicalproperty and/or seismic cube property values assigned to a first subsetof points of the first model. Editing property values may includechanging, adding, or deleting property values associated with thepoints. In one example, a user may assign or “paint” a geologicalproperty value with a brush onto horizons in present day G space or pastdepositional G* space (e.g., using editing tools such as brushes 142 or144, respectively), e.g., assigning a property value, e.g., Gprop1, tothe points traced by the brush. In another example, a user may delete or“erase” a property value with a brush onto horizons in G space or G*space (e.g., using brushes 142 or 144, respectively), e.g., resetting orre-assigning the property value to a previously assigned or defaultvalue. e.g., Gprop0. Multiple different properties may be changed.

In operation 1140, the computing device may automatically assign thesame edited property values to a second subset of points of the secondmodel, where the second subset of points are the image of the firstsubset of points as defined by the transformation between the first andsecond models. In the example where the brush is in a painting mode,assigning property values. Gprop1, to the first subset of points, thecomputing device may automatically assign the same property values,Gprop1, to the image of the first set of points under thetransformation. In the example where the brush is in an erasing mode,resetting property values, Gprop0, to the first subset of points, thecomputing device may automatically reset the same property values,Gprop0, to the image of the first set of points under thetransformation.

Accordingly, when a property value is assigned to a first point in thefirst model, the same property value may be assigned to a second point(e.g., the image of the first point) in the second model. The propertyvalues of the first and second subsets of points may be edited withoutaltering the transformation between the first and second models.

In operation 1150, a display device (e.g. display 980 of FIG. 9) maydisplay the second subset of points in the second model with theautomatically assigned property values. Optionally, the display devicemay also display the first model.

The computing device may accept the data used in the aforementionedoperations as for example a set of data reflected from a subsurfacegeological feature, or such data augmented by another process.

In contrast to embodiments described in reference to FIG. 10, in whichthe locations of points or features (e.g., horizons) are changed, e.g.,by moving, adding, deleting or otherwise changing location features ofthe models, in embodiments described in FIG. 11, the locations of thepoints may be left unchanged and only the property values of the pointsare changed. Furthermore, in contrast to embodiments described inreference to FIG. 10, in which edits to the model cause thetransformation that relates the two models to be changed, in embodimentsdescribed in FIG. 11, the transformation that relates the two models istypically not changed. Although these are provided in some embodiments,in other embodiments features from embodiments of FIGS. 10 and 11 may becombined. For example, points forming non-uniform property values acrosshorizons in G space or horizontal cross sections in G* space may beremoved or moved in the model (e.g., according to embodiments of FIG.10) or may have their property values changed so that they match theproperty values of the other points in the horizons or horizontal crosssections (e.g., according to embodiments of FIG. 11). In one example,when a color map is used, e.g., red corresponding to one property valueGprop1 and purple to another property value Gprop2, a stray point mayappear as a purple dot in an otherwise red horizontal section. Accordingto embodiments of FIG. 10, a user may choose to replace the point havingproperty value Gprop2 represented by a purple dot with another pointhaving property value Gprop1 represented by a red dot, e.g., by clickingon the purple dot in a ‘delete’ mode, and clicking a neighboring red dotactivate in an ‘add’ mode. According to embodiments of FIG. 11, a usermay select the property value Gprop1 represented by red, activate the“paint” mode and trace a brush over the purple dot to change theproperty value associated therewith from Gprop2 (purple) to Gprop1(red). The user may identify points to be changed via input device 965of FIG. 9, e.g., controlled to click on or otherwise select the pointson display 980 of FIG. 9.

In an embodiment of the invention, a method and system is provided formodelling physical geological structures. Seismic data (e.g., storedwith seismic cubes) and/or geologic data (e.g., well markers along wellpaths) may be accepted. A 3D transformation may be generated between a3D present day model having points representing present locations of thephysical geological structures and a 3D past depositional model havingpoints representing locations where the physical geological structureswere originally deposited. An indication may be accepted to locallychange the 3D transformation for a subset of points in a first model ofthe models. The 3D transformation may be locally changed for the subsetof points, for example, by adding, removing or moving existing samplingpoints. The uvt-transformation may be updated to take the new set ofsampling points into account. A locally altered or updated version ofthe first model may be displayed. Local changes to the first model maybe defined by the locally changed 3D transformation.

Updating or locally changing the transformation to take into account anedited subset of sampling points in a first model and may cause theimage of those points in the second model to be changed to pointsdifferent than the image points defined by the initial transformation.

Locally changing the 3D transformation for the subset of points maycause the subset of points to be deleted or removed from the first modeland the image points of the subset of points under the 3D transformationto be deleted or removed from a second model of the models. Locallychanging the 3D transformation for the subset of points may cause thesubset of points to be added to the first model and the image points ofthe subset of points under the 3D transformation to be added to a secondmodel of the models. Locally changing the 3D transformation for thesubset of points in the first model may cause the image of those pointsin a second model of the models to be changed to points different thanthe image points defined by the initial 3D transformation.

The subset of points may be replaced with a new subset of points in thefirst model (e.g., in G space or G* space) and a subset of pointscorresponding to the transformation (e.g., reverse uvt-transformation orforward uvt-transformation, respectively) of the replaced subset ofpoints may be replaced with a new subset of points corresponding to thereverse transformation of the new subset of points in a second model ofthe models (e.g., in G* space or G space, respectively).

In response to accepting the indication to locally change the subset ofpoints in the first model, points in a second model of the models fromwhich the subset of points are transformed by the changed 3Dtransformation may be updated, e.g. automatically.

The subset of points may be selected. e.g., automatically, from the pastdepositional model by for example a computing device to be points havingproperty values that are different than the property values of otherpoints located on the same horizon or horizontal cross-section of thepast depositional model. The property values may be stored associatedwith the storage of cells of the past depositional model.

In an embodiment of the invention, a method and device is provided forsimultaneously editing corresponding models representing the samephysical geological structures. Seismic data (e.g., stored with seismiccubes) and/or geologic data (e.g., well markers along well paths) may beaccepted. A first model and a second model may be displayed. One of themodels may represent present day locations of the physical geologicalstructures and the other one of the models may represent locations wherethe physical geological structures were originally deposited in thepast. The first and second models may be related by a 3D transformation.Graphical user input may be accepted for editing property valuesassigned to a first subset of points of the first model. The editedproperty values may be automatically assigned to a second subset ofpoints of the second model, where the second subset of points are theimage of the first subset of points as defined by the 3D transformationbetween the first and second models. The second subset of points may bedisplayed in the second model with the automatically assigned propertyvalues.

When one property value is assigned to a first point in the first model,the same property value may be assigned to a second point in the secondmodel, wherein the second point is the image of the first point asdefined by the 3D transformation between the first and second models.Editing property values may include changing, adding, removing ordeleting property values. The same property values may be assigned topoints in the first and second models which are each other's imagesunder the 3D transformation. The property values may be associated witha geobody.

The graphical user input may be generated in a for example computingdevice using a graphical editing tool. The property values of the firstand second subsets of points may be painted on or erased from at leastone of the models using the graphical editing tool without altering thelocations of points in the first and second models.

Property values may first be edited in the past depositional model andthen automatically edited in the present location model or may first beedited in the present location model and then automatically edited inthe past depositional model. When the property values associated with ageobody are first edited at points in the past depositional model thatcorrespond to points on opposite sides of a fault of the presentlocation model, the property values associated with a geobody may beautomatically edited to extend across opposite sides of the fault.

In an embodiment of the invention, a memory or other storage device maybe provided to store a 3D transformation between a 3D present day modelhaving points representing present locations of the physical geologicalstructures and a 3D past depositional model having points representinglocations where the physical geological structures were originallydeposited. A processor or controller may be provided to accept anindication to locally change the 3D transformation for a subset ofpoints in a first model of the models and to locally change the 3Dtransformation for the subset of points. A display may be provided todisplay a locally altered version the first model. Local changes to thefirst model may be defined by the locally changed 3D transformation.

The processor may locally change or update the 3D transformation to fita new updated set of sampling points. The processor may locally changethe 3D transformation for the new updated subset of points by deletingthe subset of points from the first model and deleting the image pointsof the subset of points under the 3D transformation from a second modelof the models. The processor may locally change the 3D transformationfor the subset of points by adding the subset of points to the firstmodel and adding the image points of the subset of points under the 3Dtransformation to a second model of the models. The processor maylocally change the 3D transformation for the subset of points bychanging the image of those points in a second model of the models topoints different than the image points defined by the initial 3Dtransformation.

The processor may replace the subset of points with a new subset ofpoints in the first model (e.g., in G space or G* space) and may replacea subset of points corresponding to the transformation (e.g., reverseuvt-transformation or forward uvt-transformation, respectively) of thereplaced subset of points with a new subset of points corresponding tothe reverse transformation of the new subset of points in a second modelof the models (e.g., in G* space or G space, respectively).

In response to accepting the indication to update or locally change thesubset of points in the first model, the processor may automaticallyupdate points in a second model of the models from which the subset ofpoints are transformed by the locally changed 3D transformation.

The processor may automatically select the subset of points from thepast depositional model to be points having property values that aredifferent than the property values of other points located on the samehorizon or horizontal cross-section of the past depositional model.

The processor may accept graphical user input editing property valuesassigned to the subset of points of the first model and mayautomatically assign edited property values to a second subset of pointsof a second model of the models. The second subset of points may be theimage of the first subset of points as defined by the 3D transformationbetween the first and second models.

In the foregoing description, various aspects of the present inventionhave been described. For purposes of explanation, specificconfigurations and details have been set forth in order to provide athorough understanding of the present invention. However, it will alsobe apparent to one skilled in the art that the present invention may bepracticed without the specific details presented herein. Furthermore,well known features may have been omitted or simplified in order not toobscure the present invention. Unless specifically stated otherwise, asapparent from the following discussions, it is appreciated thatthroughout the specification discussions utilizing terms such as“processing,” “computing,” “calculating.” “determining,” or the like,refer to the action and/or processes of a computer or computing system,or similar electronic computing device, that manipulates and/ortransforms data represented as physical, such as electronic, quantitieswithin the computing system's registers and/or memories into other datasimilarly represented as physical quantities within the computingsystem's memories, registers or other such information storage,transmission or display devices. In addition, the term “plurality” maybe used throughout the specification to describe two or more components,devices, elements, parameters and the like.

Embodiments of the invention may manipulate data representations ofreal-world objects and entities such as underground geological features,including faults, horizons and other features. Data received by forexample a receiver receiving waves generated by an air gun or explosivesmay be manipulated and stored, e.g., in memory 950, and data such asimages representing underground features may be presented to a user.e.g., as a visualization on display 980.

When used herein, geological features such as horizons and faults mayrefer to the actual geological feature existing in the real world, orcomputer data representing such features (e.g., stored in a memory ormass storage device). Some features when represented in a computingdevice may be approximations or estimates of a real world feature, or avirtual or idealized feature, such as an idealized horizon as producedin a uvt-transform. A model, or a model representing subsurface featuresor the location of those features, is typically an estimate or a“model”, which may approximate or estimate the physical subsurfacestructure being modeled with more or less accuracy.

It should be recognized that embodiments of the present invention maysolve one or more of the objectives and/or challenges described in thebackground, and that embodiments of the invention need not meet everyone of the above objectives and/or challenges to come within the scopeof the present invention. Various embodiments have been presented. Eachof these embodiments may of course include features from otherembodiments presented, and embodiments not specifically described mayinclude various features described herein. While certain features of theinvention have been particularly illustrated and described herein, manymodifications, substitutions, changes, and equivalents may occur tothose of ordinary skill in the art. It is, therefore, to be understoodthat the appended claims are intended to cover all such modificationsand changes in form and details as fall within the true spirit of theinvention.

The invention claimed is:
 1. A method of editing a dual model ofphysical geological structures using a pair of twin three-dimensional(3D) volume painters, the method comprising: accepting geological data;generating a dual model comprising a 3D present day model having pointsrepresenting present locations of the physical geological structures anda 3D past depositional model having points representing locations wherethe physical geological structures were computed to be originallydeposited; generating a pair of twin 3D volume painters comprising onepresent day painter volume located in the 3D present day model andanother past depositional painter volume located in the 3D pastdepositional model, wherein the pair of painter volumes are related by a3D transformation between the 3D present day model and the 3D pastdepositional model; and displaying the pair of twin 3D volume painterssuch that the present day painter volume and the past depositionalpainter volume are simultaneously centered on a pair of respectivepoints of the dual model, wherein the center of the present day paintervolume is the forward 3D transformation of the center of the pastdepositional painter volume and the center of the past depositionalpainter volume is the reverse 3D transformation of the center of thepresent day painter volume.
 2. The method of claim 1, wherein when thepresent day painter volume is moved or used in the 3D present day model,a simultaneous and corresponding movement or usage is executed in the 3Dpast depositional model, and vice versa.
 3. The method of claim 1,wherein when the past depositional painter volume crosses thetransformation of a fault in the 3D past depositional model, the presentday painter volume includes multiple disconnected volumes on both sidesof the fault in the 3D present day model.
 4. The method of claim 1,wherein editing the dual model comprises operating the pair of twin 3Dvolume painters in painting or erasing modes to edit the seismic orgeological property data of the 3D present day model and the 3D pastdepositional model.
 5. The method of claim 1, wherein the present daypainter volume is moved onto and across a faulted horizon in the 3Dpresent day model and the past depositional painter volume is moved ontoand across a flattened horizon that is the transformation image of thefaulted horizon in the 3D past depositional model.
 6. The method ofclaim 5, wherein: in the 3D past depositional model, the pastdepositional painter volume moving onto the flattened horizon includes:top and bottom faces located on adjacent horizons above and below theflattened horizon, respectively, and vertical lateral faces; and in the3D present day model, the present day painter volume moving onto thefaulted horizon includes: top and bottom faces located on adjacenthorizons above and below the faulted horizon respectively, and lateralfaces tangential to Iso-Paleo-Geographic (IPG) lines that arecurvilinear in the 3D present day model and transformed from verticalstraight-lines in the 3D past depositional model under thetransformation.
 7. The method of claim 1 comprising activating the pairof twin 3D volume painters in response to user input.
 8. The method ofclaim 1, wherein the pair of twin 3D volume painters have a shapeselected from the group consisting of: a sphere, half a sphere, anellipsoid, half an ellipsoid, a polyhedron, and a prism.
 9. The methodof claim 1 comprising receiving selection by a user of a size or shapeof the pair of twin 3D volume painters.
 10. The method of claim 1comprising displaying the present day painter volume and the pastdepositional painter volume on adjacent windows on a computer screenwith the corresponding 3D present day model and 3D past depositionalmodel, respectively.
 11. A system comprising: a memory configured tostore a dual model comprising a 3D present day model having pointsrepresenting present locations of physical geological structures and a3D past depositional model having points representing locations wherethe physical geological structures were computed to be originallydeposited; and one or more processors configured to: generate a pair oftwin 3D volume painters comprising one present day painter volumelocated in the 3D present day model and another past depositionalpainter volume located in the 3D past depositional model, wherein thepair of painter volumes are related by a 3D transformation between the3D present day model and the 3D past depositional model, and display thepair of twin 3D volume painters such that the present day painter volumeand the past depositional painter volume are simultaneously centered ona pair of respective points of the dual model, wherein the center of thepresent day painter volume is the forward 3D transformation of thecenter of the past depositional painter volume and the center of thepast depositional painter volume is the reverse 3D transformation of thecenter of the present day painter volume.
 12. The system of claim 11,wherein when the present day painter volume is moved or used in the 3Dpresent day model, the one or more processors are configured to executea simultaneous and corresponding movement or usage in the 3D pastdepositional model and vice versa.
 13. The system of claim 11, whereinwhen the past depositional painter volume crosses the transformation ofa fault in the 3D past depositional model, the one or more processorsare configured to generate the present day painter volume to havemultiple disconnected volumes on both sides of the fault in the 3Dpresent day model.
 14. The system of claim 11, wherein the one or moreprocessors are configured to edit the dual model by operating the pairof twin 3D volume painters in painting or erasing modes to edit theseismic or geological property data of the 3D present day model and the3D past depositional model.
 15. The system of claim 11, wherein the oneor more processors are configured to move the present day painter volumeonto and across a faulted horizon in the 3D present day model and movethe past depositional painter volume onto and across a flattened horizonthat is the transformation image of the faulted horizon in the 3D pastdepositional model.
 16. The system of claim 15, wherein the one or moreprocessors are configured to generate the pair of twin 3D volumepainters such that: in the 3D past depositional model the pastdepositional painter volume moving onto the flattened horizon includes:top and bottom faces located on adjacent horizons above and below theflattened horizon, respectively, and vertical lateral faces, and in the3D present day model, the present day painter volume moving onto thefaulted horizon includes: top and bottom faces located on adjacenthorizons above and below the faulted horizon respectively, and lateralfaces tangential to Iso-Paleo-Geographic (IPG) lines that arecurvilinear in the 3D present day model and transformed from verticalstraight-lines in the 3D past depositional model under thetransformation.
 17. The system of claim 11, wherein the one or moreprocessors are configured to activate the pair of twin 3D volumepainters in response to user input from an input device.
 18. The systemof claim 11, wherein the one or more processors are configured togenerate the pair of twin 3D volume painters that have a shape selectedfrom the group consisting of: a sphere, half a sphere, an ellipsoid,half an ellipsoid, a polyhedron, and a prism.
 19. The system of claim11, wherein the one or more processors are configured to receiveselection by a user of a size or shape of the pair of twin 3D volumepainters.
 20. The system of claim 11, wherein the one or more processorsare configured to display the present day painter volume and the pastdepositional painter volume on adjacent windows on a computer screenwith the corresponding 3D present day model and 3D past depositionalmodel, respectively.